chore: release v0.4.0

.github/workflows/ci.yml

@@ -6,6 +6,9 @@ on:
   pull_request:
     branches: [main, master]
 
+permissions:
+  contents: read
+
 env:
   CARGO_TERM_COLOR: always
 
@@ -58,6 +61,21 @@ jobs:
             cargo test --verbose --features "${{ matrix.features }}"
           fi
 
+  examples:
+    name: Examples
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v6
+      - name: Install Rust
+        run: |
+          rustup override set stable
+          rustup update stable
+      - uses: Swatinem/rust-cache@v2
+      - name: Run sync example (ml_hyperparameter_tuning)
+        run: cargo run --example ml_hyperparameter_tuning
+      - name: Run async example (async_api_optimization)
+        run: cargo run --example async_api_optimization --features async
+
   docs:
     name: Docs
     runs-on: ubuntu-latest
@@ -240,6 +258,7 @@ jobs:
       - fmt
       - clippy
       - test
+      - examples
       - docs
       - feature-check
       - coverage
@@ -275,7 +294,14 @@ jobs:
           fi
 
       - name: Publish
-        if: steps.check.outputs.skip == 'false' && github.ref == 'refs/heads/master'
-        run: cargo publish
+        if: steps.check.outputs.skip == 'false'
+        run: |
+          cargo publish --allow-dirty 2>&1 | tee publish_output.txt || {
+            if grep -q "already uploaded" publish_output.txt; then
+              echo "Version already published, skipping"
+              exit 0
+            fi
+            exit 1
+          }
         env:
           CARGO_REGISTRY_TOKEN: ${{ secrets.CARGO_REGISTRY_TOKEN }}

.github/workflows/scheduled.yml

@@ -5,6 +5,9 @@ on:
     - cron: "0 6 * * *" # Daily at 6:00 UTC
   workflow_dispatch: # Allow manual trigger
 
+permissions:
+  contents: read
+
 env:
   CARGO_TERM_COLOR: always
 

Cargo.toml

@@ -1,15 +1,19 @@
 [package]
 name = "optimizer"
-version = "0.3.0"
+version = "0.4.0"
 edition = "2024"
 rust-version = "1.88"
 license = "MIT"
 authors = ["Manuel Raimann <raimannma@outlook.de"]
 description = "A Rust library for optimization algorithms."
 repository = "https://github.com/raimannma/rust-optimizer"
-
+documentation = "https://docs.rs/optimizer"
+keywords = ["optimization", "hyperparameter", "tpe", "grid-search", "bayesian"]
+categories = ["algorithm", "science", "data-structures"]
+readme = "README.md"
 
 [dependencies]
+log = "0.4"
 rand = "0.9"
 thiserror = "2"
 parking_lot = "0.12"
@@ -20,4 +24,13 @@ default = []
 async = ["dep:tokio"]
 
 [dev-dependencies]
-tokio = { version = "1", features = ["rt-multi-thread", "macros"] }
+tokio = { version = "1", features = ["rt-multi-thread", "macros", "time"] }
+
+[[example]]
+name = "async_api_optimization"
+path = "examples/async_api_optimization.rs"
+required-features = ["async"]
+
+[[example]]
+name = "ml_hyperparameter_tuning"
+path = "examples/ml_hyperparameter_tuning.rs"

README.md

@@ -1,6 +1,6 @@
 # optimizer
 
-A Rust library for black-box optimization using Tree-Parzen Estimator (TPE).
+A Rust library for black-box optimization with multiple sampling strategies.
 
 [![Docs](https://docs.rs/optimizer/badge.svg)](https://docs.rs/optimizer)
 [![Crates.io](https://img.shields.io/crates/v/optimizer.svg)](https://crates.io/crates/optimizer)
@@ -9,6 +9,10 @@ A Rust library for black-box optimization using Tree-Parzen Estimator (TPE).
 ## Features
 
 - Optuna-like API for hyperparameter optimization
+- Multiple sampling strategies:
+  - **Random Search** - Simple random sampling for baseline comparisons
+  - **TPE (Tree-Parzen Estimator)** - Bayesian optimization for efficient search
+  - **Grid Search** - Exhaustive search over a specified parameter grid
 - Float, integer, and categorical parameter types
 - Log-scale and stepped parameter sampling
 - Sync and async optimization with parallel trial evaluation
@@ -16,15 +20,16 @@ A Rust library for black-box optimization using Tree-Parzen Estimator (TPE).
 ## Quick Start
 
 ```rust
-use optimizer::{Direction, Study, TpeSampler};
+use optimizer::{Direction, Study};
+use optimizer::sampler::tpe::TpeSampler;
 
-let sampler = TpeSampler::builder().seed(42).build();
+let sampler = TpeSampler::builder().seed(42).build().unwrap();
 let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
 
 study
     .optimize_with_sampler(20, |trial| {
         let x = trial.suggest_float("x", -10.0, 10.0)?;
-        Ok::<_, optimizer::TpeError>(x * x)
+        Ok::<_, optimizer::Error>(x * x)
     })
     .unwrap();
 
@@ -32,6 +37,100 @@ let best = study.best_trial().unwrap();
 println!("Best value: {} at x={:?}", best.value, best.params);
 ```
 
+## Samplers
+
+### Random Search
+
+```rust
+use optimizer::{Direction, Study};
+use optimizer::sampler::random::RandomSampler;
+
+let study: Study<f64> = Study::with_sampler(
+    Direction::Minimize,
+    RandomSampler::with_seed(42),
+);
+```
+
+### TPE (Tree-Parzen Estimator)
+
+```rust
+use optimizer::{Direction, Study};
+use optimizer::sampler::tpe::TpeSampler;
+
+let sampler = TpeSampler::builder()
+    .gamma(0.15)           // Quantile for good/bad split
+    .n_startup_trials(20)  // Random trials before TPE kicks in
+    .n_ei_candidates(32)   // Candidates to evaluate
+    .seed(42)
+    .build()
+    .unwrap();
+
+let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+```
+
+#### Gamma Strategies
+
+The gamma parameter controls what fraction of trials are considered "good" when building the TPE model. Instead of a fixed value, you can use adaptive strategies:
+
+| Strategy | Description | Formula |
+|----------|-------------|---------|
+| `FixedGamma` | Constant value (default: 0.25) | `γ = constant` |
+| `LinearGamma` | Linear interpolation over trials | `γ = γ_min + (γ_max - γ_min) * min(n/n_max, 1)` |
+| `SqrtGamma` | Optuna-style inverse sqrt scaling | `γ = min(γ_max, factor/√n / n)` |
+| `HyperoptGamma` | Hyperopt-style adaptive | `γ = min(γ_max, (base + 1) / n)` |
+
+```rust
+use optimizer::sampler::tpe::{TpeSampler, SqrtGamma, LinearGamma};
+
+// Optuna-style gamma that decreases with more trials
+let sampler = TpeSampler::builder()
+    .gamma_strategy(SqrtGamma::default())
+    .build()
+    .unwrap();
+
+// Linear interpolation from 0.1 to 0.3 over 100 trials
+let sampler = TpeSampler::builder()
+    .gamma_strategy(LinearGamma::new(0.1, 0.3, 100).unwrap())
+    .build()
+    .unwrap();
+```
+
+You can also implement custom strategies:
+
+```rust
+use optimizer::sampler::tpe::{TpeSampler, GammaStrategy};
+
+#[derive(Debug, Clone)]
+struct MyGamma { base: f64 }
+
+impl GammaStrategy for MyGamma {
+    fn gamma(&self, n_trials: usize) -> f64 {
+        (self.base + 0.01 * n_trials as f64).min(0.5)
+    }
+    fn clone_box(&self) -> Box<dyn GammaStrategy> {
+        Box::new(self.clone())
+    }
+}
+
+let sampler = TpeSampler::builder()
+    .gamma_strategy(MyGamma { base: 0.1 })
+    .build()
+    .unwrap();
+```
+
+### Grid Search
+
+```rust
+use optimizer::{Direction, Study};
+use optimizer::sampler::grid::GridSearchSampler;
+
+let sampler = GridSearchSampler::builder()
+    .n_points_per_param(10)  // Number of points per parameter dimension
+    .build();
+
+let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+```
+
 ## Feature Flags
 
 - `async` - Enable async optimization methods (requires tokio)

examples/async_api_optimization.rs

@@ -0,0 +1,317 @@
+//! Async API Parameter Optimization Example
+//!
+//! This example shows how to use async/parallel optimization to tune
+//! configuration parameters for a web service. Each evaluation simulates
+//! an async operation (like deploying and load-testing a service).
+//!
+//! # Key Concepts Demonstrated
+//!
+//! - Async optimization with `optimize_parallel_with_sampler`
+//! - Running multiple trials concurrently for faster optimization
+//! - Boolean and categorical parameter types
+//! - Measuring speedup from parallelism
+//!
+//! # When to Use Async Optimization
+//!
+//! Use async/parallel optimization when your objective function involves:
+//! - Network requests (API calls, database queries)
+//! - File I/O operations
+//! - External service calls
+//! - Any operation where you're waiting for I/O rather than computing
+//!
+//! With parallelism, you can evaluate multiple configurations simultaneously,
+//! significantly reducing total optimization time.
+//!
+//! Run with: `cargo run --example async_api_optimization --features async`
+
+use std::time::{Duration, Instant};
+
+use optimizer::sampler::tpe::TpeSampler;
+use optimizer::{Direction, ParamValue, Study, Trial};
+
+// ============================================================================
+// Configuration: Service parameters we want to tune
+// ============================================================================
+
+/// Configuration for a web service.
+///
+/// In a real application, these parameters would control:
+/// - Memory allocation (cache sizes)
+/// - Connection management (pool sizes, timeouts)
+/// - Request handling (batching, compression)
+/// - Protocol options (HTTP version, load balancing)
+struct ServiceConfig {
+    cache_size_mb: i64,
+    connection_pool_size: i64,
+    request_timeout_ms: i64,
+    retry_count: i64,
+    batch_size: i64,
+    compression_level: i64,
+    use_http2: bool,
+    load_balancing: String,
+}
+
+// ============================================================================
+// Objective Function: Evaluate a service configuration
+// ============================================================================
+
+/// Simulates deploying and load-testing a service configuration.
+///
+/// In a real scenario, this function might:
+/// 1. Deploy the configuration to a staging environment
+/// 2. Run load tests against the service
+/// 3. Collect metrics (latency, throughput, error rate)
+/// 4. Return a composite score
+///
+/// The async sleep simulates the I/O time of these operations.
+/// This is where parallel execution helps - while one trial is waiting
+/// for I/O, other trials can run.
+#[allow(clippy::too_many_arguments)]
+async fn evaluate_service(config: &ServiceConfig) -> f64 {
+    // Simulate async I/O (deployment, load testing, metric collection)
+    tokio::time::sleep(Duration::from_millis(50)).await;
+
+    // Calculate a score based on how close we are to optimal values
+    // Lower score = better configuration
+    let mut score = 0.0;
+
+    // Cache size: too small = cache misses, too large = wasted memory
+    // Optimal around 512MB
+    let cache_optimal = 512.0;
+    score += ((config.cache_size_mb as f64 - cache_optimal) / 256.0).powi(2);
+
+    // Connection pool: too small = contention, too large = resource waste
+    // Optimal around 100
+    let pool_optimal = 100.0;
+    score += ((config.connection_pool_size as f64 - pool_optimal) / 50.0).powi(2);
+
+    // Timeout: too short = false failures, too long = slow recovery
+    // Optimal around 5000ms
+    let timeout_optimal = 5000.0;
+    score += ((config.request_timeout_ms as f64 - timeout_optimal) / 2000.0).powi(2);
+
+    // Retries: too few = fragile, too many = amplifies failures
+    // Optimal around 3
+    let retry_optimal = 3.0;
+    score += ((config.retry_count as f64 - retry_optimal) / 2.0).powi(2);
+
+    // Batch size: trade-off between latency and throughput
+    // Optimal around 64
+    let batch_optimal = 64.0;
+    score += ((config.batch_size as f64 - batch_optimal) / 32.0).powi(2);
+
+    // Compression level: trade-off between CPU and bandwidth
+    // Optimal around 6
+    let compression_optimal = 6.0;
+    score += ((config.compression_level as f64 - compression_optimal) / 3.0).powi(2);
+
+    // HTTP/2 is generally better for our use case
+    if !config.use_http2 {
+        score += 0.5;
+    }
+
+    // Load balancing strategy affects performance
+    score += match config.load_balancing.as_str() {
+        "round_robin" => 0.0,       // Best for our use case
+        "least_connections" => 0.1, // Good alternative
+        "ip_hash" => 0.2,           // OK for session affinity
+        "random" => 0.3,            // Not ideal
+        _ => 1.0,
+    };
+
+    // Add noise to simulate real-world variability
+    let noise = (config.cache_size_mb as f64 * 0.1).sin() * 0.05;
+
+    score + noise
+}
+
+/// The async objective function for each trial.
+///
+/// For async optimization, the objective function must:
+/// 1. Take ownership of the Trial (not a mutable reference)
+/// 2. Return a Future
+/// 3. Return both the Trial and the result value as a tuple
+///
+/// This ownership pattern allows the trial to be used across await points.
+async fn objective(mut trial: Trial) -> optimizer::Result<(Trial, f64)> {
+    // Sample configuration parameters
+
+    // Stepped integers: only sample multiples of the step value
+    let cache_size_mb = trial.suggest_int_step("cache_size_mb", 64, 1024, 64)?;
+    let connection_pool_size = trial.suggest_int_step("connection_pool_size", 10, 200, 10)?;
+    let request_timeout_ms = trial.suggest_int_step("request_timeout_ms", 1000, 10000, 500)?;
+
+    // Regular integer
+    let retry_count = trial.suggest_int("retry_count", 0, 5)?;
+
+    // Log-scale integer: good for parameters like batch sizes
+    // that might vary from 1 to 256
+    let batch_size = trial.suggest_int_log("batch_size", 1, 256)?;
+
+    // Regular integer for compression level
+    let compression_level = trial.suggest_int("compression_level", 0, 9)?;
+
+    // Boolean: internally uses categorical with [false, true]
+    let use_http2 = trial.suggest_bool("use_http2")?;
+
+    // Categorical: choose from a list of options
+    let load_balancing = trial.suggest_categorical(
+        "load_balancing",
+        &["round_robin", "least_connections", "random", "ip_hash"],
+    )?;
+
+    // Build configuration
+    let config = ServiceConfig {
+        cache_size_mb,
+        connection_pool_size,
+        request_timeout_ms,
+        retry_count,
+        batch_size,
+        compression_level,
+        use_http2,
+        load_balancing: load_balancing.to_string(),
+    };
+
+    // Evaluate (this is the async part)
+    let score = evaluate_service(&config).await;
+
+    // Return both the trial and the score
+    Ok((trial, score))
+}
+
+// ============================================================================
+// Helper Functions
+// ============================================================================
+
+/// Formats a parameter value for display.
+fn format_param(name: &str, value: &ParamValue) -> String {
+    match (name, value) {
+        (_, ParamValue::Float(v)) => format!("{v:.4}"),
+        (_, ParamValue::Int(v)) => format!("{v}"),
+        ("use_http2", ParamValue::Categorical(idx)) => {
+            if *idx == 1 { "true" } else { "false" }.to_string()
+        }
+        ("load_balancing", ParamValue::Categorical(idx)) => {
+            ["round_robin", "least_connections", "random", "ip_hash"]
+                .get(*idx)
+                .unwrap_or(&"unknown")
+                .to_string()
+        }
+        (_, ParamValue::Categorical(idx)) => format!("category_{idx}"),
+    }
+}
+
+/// Prints the results of the optimization.
+fn print_results(study: &Study<f64>, elapsed: Duration, n_trials: usize) {
+    println!("\n{}", "=".repeat(60));
+    println!("\nOptimization completed!");
+    println!("Total trials: {}", study.n_trials());
+    println!("Time elapsed: {elapsed:.2?}");
+
+    // Calculate speedup from parallelism
+    // Each trial takes ~50ms, so sequential would take n_trials * 50ms
+    let sequential_time = n_trials as f64 * 0.050;
+    let actual_time = elapsed.as_secs_f64();
+    println!(
+        "Effective parallelism: {:.1}x speedup",
+        sequential_time / actual_time
+    );
+}
+
+/// Prints the best configuration found.
+fn print_best_config(study: &Study<f64>) -> optimizer::Result<()> {
+    let best = study.best_trial()?;
+
+    println!("\nBest configuration found:");
+    println!("  Score: {:.6}", best.value);
+    println!("\n  Parameters:");
+
+    // Print parameters in a logical order
+    let param_order = [
+        "cache_size_mb",
+        "connection_pool_size",
+        "request_timeout_ms",
+        "retry_count",
+        "batch_size",
+        "compression_level",
+        "use_http2",
+        "load_balancing",
+    ];
+
+    for name in param_order {
+        if let Some(value) = best.params.get(name) {
+            let display = format_param(name, value);
+            println!("    {name}: {display}");
+        }
+    }
+
+    Ok(())
+}
+
+/// Prints the top N trials.
+fn print_top_trials(study: &Study<f64>, n: usize) {
+    println!("\nTop {n} trials:");
+
+    let mut trials = study.trials();
+    trials.sort_by(|a, b| a.value.partial_cmp(&b.value).unwrap());
+
+    for (i, trial) in trials.iter().take(n).enumerate() {
+        println!(
+            "  {}. Trial #{}: score = {:.6}",
+            i + 1,
+            trial.id,
+            trial.value
+        );
+    }
+}
+
+// ============================================================================
+// Main: Set up and run the async optimization
+// ============================================================================
+
+#[tokio::main]
+async fn main() -> optimizer::Result<()> {
+    println!("=== Async API Parameter Optimization Example ===\n");
+
+    // Step 1: Create a TPE sampler
+    let sampler = TpeSampler::builder()
+        .n_startup_trials(8)
+        .gamma(0.2)
+        .seed(123)
+        .build()
+        .expect("Failed to build TPE sampler");
+
+    // Step 2: Create a study to minimize the score
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+
+    // Step 3: Configure optimization
+    let n_trials = 40;
+    let concurrency = 4; // Run 4 trials in parallel
+
+    println!("Starting parallel optimization with {concurrency} concurrent evaluations...\n");
+
+    let start = Instant::now();
+
+    // Step 4: Run parallel async optimization
+    //
+    // optimize_parallel_with_sampler:
+    // - Runs up to `concurrency` trials simultaneously
+    // - Each trial calls the objective function
+    // - Uses a semaphore to limit concurrent evaluations
+    // - Collects results as trials complete
+    //
+    // The "_with_sampler" suffix means the TPE sampler gets access to
+    // trial history for informed sampling.
+    study
+        .optimize_parallel_with_sampler(n_trials, concurrency, objective)
+        .await?;
+
+    let elapsed = start.elapsed();
+
+    // Step 5: Print results
+    print_results(&study, elapsed, n_trials);
+    print_best_config(&study)?;
+    print_top_trials(&study, 5);
+
+    Ok(())
+}

examples/ml_hyperparameter_tuning.rs

@@ -0,0 +1,269 @@
+//! Machine Learning Hyperparameter Tuning Example
+//!
+//! This example shows how to use the optimizer library to find the best
+//! hyperparameters for a machine learning model. We simulate a gradient
+//! boosting model (like XGBoost or LightGBM) and search for optimal settings.
+//!
+//! # Key Concepts Demonstrated
+//!
+//! - Creating a Study with a TPE (Tree-Parzen Estimator) sampler
+//! - Defining an objective function that the optimizer will minimize
+//! - Using different parameter types: floats, integers, log-scale, stepped
+//! - Using callbacks to monitor progress and implement early stopping
+//!
+//! # How It Works
+//!
+//! 1. Create a `Study` - this manages the optimization process
+//! 2. Define an objective function that takes a `Trial` and returns a score
+//! 3. Inside the objective, use `trial.suggest_*()` to sample parameters
+//! 4. The optimizer runs many trials, learning which parameter regions work best
+//! 5. After optimization, retrieve the best parameters found
+//!
+//! Run with: `cargo run --example ml_hyperparameter_tuning`
+
+use std::ops::ControlFlow;
+
+use optimizer::sampler::CompletedTrial;
+use optimizer::sampler::tpe::TpeSampler;
+use optimizer::{Direction, ParamValue, Study, Trial};
+
+// ============================================================================
+// Configuration: Hyperparameters we want to tune
+// ============================================================================
+
+/// Holds all the hyperparameters for our model.
+///
+/// In a real application, you would pass these to your ML framework
+/// (e.g., XGBoost, LightGBM, scikit-learn).
+struct ModelConfig {
+    learning_rate: f64,
+    max_depth: i64,
+    n_estimators: i64,
+    subsample: f64,
+    colsample_bytree: f64,
+    min_child_weight: i64,
+    reg_alpha: f64,
+    reg_lambda: f64,
+}
+
+// ============================================================================
+// Objective Function: What we want to optimize
+// ============================================================================
+
+/// Simulates training a model and returns the validation loss.
+///
+/// In a real scenario, this function would:
+/// 1. Create a model with the given hyperparameters
+/// 2. Train it on your training data
+/// 3. Evaluate it on validation data
+/// 4. Return the validation metric (e.g., RMSE, log loss, accuracy)
+///
+/// The optimizer will try to MINIMIZE this value (we set Direction::Minimize).
+#[allow(clippy::too_many_arguments)]
+fn evaluate_model(config: &ModelConfig) -> f64 {
+    // Simulated optimal hyperparameters:
+    // learning_rate ~ 0.05, max_depth ~ 6, n_estimators ~ 200
+    // subsample ~ 0.8, colsample_bytree ~ 0.8, min_child_weight ~ 3
+    // reg_alpha ~ 0.1, reg_lambda ~ 1.0
+
+    let mut loss = 0.15; // Base loss
+
+    // Each term penalizes deviation from the optimal value
+    loss += (config.learning_rate - 0.05).powi(2) * 100.0;
+    loss += ((config.max_depth - 6) as f64).powi(2) * 0.01;
+    loss += ((config.n_estimators - 200) as f64).powi(2) * 0.00001;
+    loss += (config.subsample - 0.8).powi(2) * 10.0;
+    loss += (config.colsample_bytree - 0.8).powi(2) * 10.0;
+    loss += ((config.min_child_weight - 3) as f64).powi(2) * 0.05;
+    loss += (config.reg_alpha - 0.1).powi(2) * 5.0;
+    loss += (config.reg_lambda - 1.0).powi(2) * 2.0;
+
+    // Add some noise to simulate real-world variability
+    let noise = (config.learning_rate * 1000.0).sin() * 0.01;
+
+    loss + noise
+}
+
+/// The objective function that the optimizer calls for each trial.
+///
+/// This function:
+/// 1. Uses `trial.suggest_*()` methods to sample hyperparameter values
+/// 2. Builds a model configuration from those values
+/// 3. Evaluates the model and returns the loss
+///
+/// The optimizer learns from the results to suggest better parameters
+/// in future trials.
+fn objective(trial: &mut Trial) -> optimizer::Result<f64> {
+    // Sample hyperparameters using different strategies:
+
+    // Log-scale: Good for parameters spanning multiple orders of magnitude
+    // The learning rate might be 0.001, 0.01, or 0.1 - log-scale samples evenly across these
+    let learning_rate = trial.suggest_float_log("learning_rate", 0.001, 0.3)?;
+
+    // Regular integer: Uniformly samples from the range [3, 12]
+    let max_depth = trial.suggest_int("max_depth", 3, 12)?;
+
+    // Stepped integer: Only samples multiples of 50 (50, 100, 150, ..., 500)
+    // Useful when you only want to test specific values
+    let n_estimators = trial.suggest_int_step("n_estimators", 50, 500, 50)?;
+
+    // Regular float: Uniformly samples from [0.5, 1.0]
+    let subsample = trial.suggest_float("subsample", 0.5, 1.0)?;
+    let colsample_bytree = trial.suggest_float("colsample_bytree", 0.5, 1.0)?;
+
+    // More parameters
+    let min_child_weight = trial.suggest_int("min_child_weight", 1, 10)?;
+    let reg_alpha = trial.suggest_float_log("reg_alpha", 1e-3, 10.0)?;
+    let reg_lambda = trial.suggest_float_log("reg_lambda", 1e-3, 10.0)?;
+
+    // Build configuration and evaluate
+    let config = ModelConfig {
+        learning_rate,
+        max_depth,
+        n_estimators,
+        subsample,
+        colsample_bytree,
+        min_child_weight,
+        reg_alpha,
+        reg_lambda,
+    };
+
+    let loss = evaluate_model(&config);
+
+    Ok(loss)
+}
+
+// ============================================================================
+// Callback Function: Monitor progress and implement early stopping
+// ============================================================================
+
+/// Called after each successful trial completes.
+///
+/// Use callbacks to:
+/// - Log progress to console or file
+/// - Save checkpoints
+/// - Implement early stopping when a good solution is found
+/// - Track metrics over time
+///
+/// Return `ControlFlow::Continue(())` to keep optimizing.
+/// Return `ControlFlow::Break(())` to stop early.
+fn on_trial_complete(study: &Study<f64>, trial: &CompletedTrial<f64>) -> ControlFlow<()> {
+    // Helper to extract parameter values
+    let get_float = |name: &str| -> f64 {
+        match trial.params.get(name) {
+            Some(ParamValue::Float(v)) => *v,
+            _ => 0.0,
+        }
+    };
+
+    let get_int = |name: &str| -> i64 {
+        match trial.params.get(name) {
+            Some(ParamValue::Int(v)) => *v,
+            _ => 0,
+        }
+    };
+
+    // Print progress
+    println!(
+        "{:>5} {:>10.5} {:>10} {:>12} {:>10.3} {:>12.3} {:>8} {:>10.4} {:>10.4} {:>12.6}",
+        study.n_trials(),
+        get_float("learning_rate"),
+        get_int("max_depth"),
+        get_int("n_estimators"),
+        get_float("subsample"),
+        get_float("colsample_bytree"),
+        get_int("min_child_weight"),
+        get_float("reg_alpha"),
+        get_float("reg_lambda"),
+        trial.value,
+    );
+
+    // Early stopping: if we find an excellent solution, stop early
+    if trial.value < 0.16 {
+        println!("\nEarly stopping: found excellent solution!");
+        return ControlFlow::Break(());
+    }
+
+    ControlFlow::Continue(())
+}
+
+// ============================================================================
+// Main: Set up and run the optimization
+// ============================================================================
+
+fn main() -> optimizer::Result<()> {
+    println!("=== ML Hyperparameter Tuning Example ===\n");
+
+    // Step 1: Create a sampler
+    //
+    // TPE (Tree-Parzen Estimator) is a Bayesian optimization algorithm.
+    // It learns from previous trials to suggest better parameters.
+    // - n_startup_trials: Number of random trials before TPE kicks in
+    // - gamma: What fraction of trials are considered "good" (lower = more selective)
+    // - seed: For reproducibility
+    let sampler = TpeSampler::builder()
+        .n_startup_trials(10)
+        .gamma(0.25)
+        .seed(42)
+        .build()
+        .expect("Failed to build TPE sampler");
+
+    // Step 2: Create a study
+    //
+    // The study manages the optimization process. We want to MINIMIZE
+    // the loss (lower is better). Use Direction::Maximize for metrics
+    // where higher is better (like accuracy).
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+
+    // Print header
+    println!("Starting hyperparameter optimization...\n");
+    println!(
+        "{:>5} {:>10} {:>10} {:>12} {:>10} {:>12} {:>8} {:>10} {:>10} {:>12}",
+        "Trial",
+        "LR",
+        "MaxDepth",
+        "Estimators",
+        "Subsample",
+        "ColSample",
+        "MinCW",
+        "Alpha",
+        "Lambda",
+        "Loss"
+    );
+    println!("{}", "-".repeat(110));
+
+    // Step 3: Run optimization
+    //
+    // optimize_with_callback_sampler runs the objective function for up to
+    // n_trials iterations. After each trial, it calls the callback.
+    // The "_sampler" suffix means the TPE sampler gets access to trial
+    // history for informed sampling.
+    let n_trials = 50;
+
+    study.optimize_with_callback_sampler(n_trials, objective, on_trial_complete)?;
+
+    // Step 4: Get the best result
+    println!("\n{}", "=".repeat(110));
+    println!("\nOptimization completed!");
+    println!("Total trials: {}", study.n_trials());
+
+    let best = study.best_trial()?;
+    println!("\nBest trial:");
+    println!("  Loss: {:.6}", best.value);
+    println!("  Parameters:");
+
+    for (name, value) in &best.params {
+        match value {
+            ParamValue::Float(v) => println!("    {name}: {v:.6}"),
+            ParamValue::Int(v) => println!("    {name}: {v}"),
+            ParamValue::Categorical(v) => println!("    {name}: category {v}"),
+        }
+    }
+
+    // Step 5: Use the best parameters (in a real app)
+    //
+    // Now you would take best.params and use them to train your final model
+    // on the full dataset.
+
+    Ok(())
+}

src/error.rs

@@ -1,10 +1,5 @@
-//! Error types for the optimizer library.
-
-use thiserror::Error;
-
-/// The error type for TPE operations.
-#[derive(Debug, Error)]
-pub enum TpeError {
+#[derive(Debug, thiserror::Error)]
+pub enum Error {
     /// Returned when the lower bound is greater than the upper bound.
     #[error("invalid bounds: low ({low}) must be less than or equal to high ({high})")]
     InvalidBounds {
@@ -51,6 +46,32 @@ pub enum TpeError {
     #[error("KDE requires at least one sample")]
     EmptySamples,
 
+    /// Returned when multivariate KDE samples have zero dimensions.
+    #[error("multivariate KDE samples must have at least one dimension")]
+    ZeroDimensions,
+
+    /// Returned when multivariate KDE samples have inconsistent dimensions.
+    #[error(
+        "dimension mismatch: expected {expected} dimensions but sample {sample_index} has {got}"
+    )]
+    DimensionMismatch {
+        /// The expected number of dimensions.
+        expected: usize,
+        /// The actual number of dimensions in the sample.
+        got: usize,
+        /// The index of the sample with mismatched dimensions.
+        sample_index: usize,
+    },
+
+    /// Returned when bandwidth vector length doesn't match the number of dimensions.
+    #[error("bandwidth dimension mismatch: expected {expected} bandwidths but got {got}")]
+    BandwidthDimensionMismatch {
+        /// The expected number of bandwidths.
+        expected: usize,
+        /// The actual number of bandwidths provided.
+        got: usize,
+    },
+
     /// Returned when an internal invariant is violated.
     #[error("internal error: {0}")]
     Internal(&'static str),
@@ -61,5 +82,4 @@ pub enum TpeError {
     TaskError(String),
 }
 
-/// A specialized Result type for TPE operations.
-pub type Result<T> = core::result::Result<T, TpeError>;
+pub type Result<T> = core::result::Result<T, Error>;

src/kde/mod.rs

@@ -0,0 +1,13 @@
+//! Kernel Density Estimation for parameter distributions.
+//!
+//! This module provides kernel density estimators used by TPE samplers
+//! to model probability distributions over good and bad trial regions.
+//!
+//! - [`univariate`] - Univariate (single-parameter) KDE
+//! - [`multivariate`] - Multivariate (joint-parameter) KDE for capturing parameter dependencies
+
+mod multivariate;
+mod univariate;
+
+pub(crate) use multivariate::MultivariateKDE;
+pub(crate) use univariate::KernelDensityEstimator;

src/kde/multivariate.rs

@@ -0,0 +1,921 @@
+//! Multivariate Kernel Density Estimation for joint parameter distributions.
+//!
+//! This module provides a multivariate kernel density estimator that captures
+//! dependencies between parameters. Unlike the univariate KDE which models each
+//! parameter independently, the multivariate KDE models the joint distribution
+//! to better capture correlations between parameters.
+
+use rand::Rng;
+
+use crate::error::{Error, Result};
+
+/// A multivariate Gaussian kernel density estimator for joint distributions.
+///
+/// `MultivariateKDE` estimates a joint probability density function from a set
+/// of multi-dimensional samples. This is used in multivariate TPE to model
+/// the joint distributions l(x) and g(x) across multiple parameters simultaneously,
+/// capturing their dependencies.
+///
+/// # Examples
+///
+/// ```ignore
+/// use crate::kde::MultivariateKDE;
+///
+/// // Create samples: 3 samples with 2 dimensions each
+/// let samples = vec![
+///     vec![1.0, 2.0],
+///     vec![1.5, 2.5],
+///     vec![2.0, 3.0],
+/// ];
+/// let kde = MultivariateKDE::new(samples).unwrap();
+///
+/// // Get dimensionality
+/// assert_eq!(kde.n_dims(), 2);
+/// ```
+#[allow(dead_code)] // Fields and methods will be used in subsequent stories (US-003, US-004)
+#[derive(Clone, Debug)]
+pub(crate) struct MultivariateKDE {
+    /// The sample points used to construct the KDE.
+    /// Each inner Vec is one sample with `n_dims` values.
+    samples: Vec<Vec<f64>>,
+    /// The bandwidth (standard deviation) for each dimension.
+    /// Uses a diagonal bandwidth matrix (independent bandwidths per dimension).
+    bandwidths: Vec<f64>,
+    /// The number of dimensions.
+    n_dims: usize,
+}
+
+#[allow(dead_code)] // Methods will be used in subsequent stories (US-003, US-004)
+impl MultivariateKDE {
+    /// Creates a new multivariate KDE with automatic bandwidth selection using Scott's rule.
+    ///
+    /// Scott's rule for multivariate KDE sets bandwidth per dimension as:
+    /// `h_j = n^(-1/(d+4)) * sigma_j`
+    ///
+    /// where n is the number of samples, d is the dimensionality, and `sigma_j` is the
+    /// standard deviation of the j-th dimension.
+    ///
+    /// # Errors
+    ///
+    /// Returns `Error::EmptySamples` if `samples` is empty.
+    /// Returns `Error::DimensionMismatch` if samples have inconsistent dimensions.
+    /// Returns `Error::ZeroDimensions` if samples have zero dimensions.
+    #[allow(clippy::cast_precision_loss)]
+    pub(crate) fn new(samples: Vec<Vec<f64>>) -> Result<Self> {
+        if samples.is_empty() {
+            return Err(Error::EmptySamples);
+        }
+
+        let n_dims = samples[0].len();
+        if n_dims == 0 {
+            return Err(Error::ZeroDimensions);
+        }
+
+        // Check all samples have the same dimensionality
+        for (i, sample) in samples.iter().enumerate() {
+            if sample.len() != n_dims {
+                return Err(Error::DimensionMismatch {
+                    expected: n_dims,
+                    got: sample.len(),
+                    sample_index: i,
+                });
+            }
+        }
+
+        let bandwidths = Self::scotts_rule_multivariate(&samples, n_dims);
+
+        Ok(Self {
+            samples,
+            bandwidths,
+            n_dims,
+        })
+    }
+
+    /// Creates a new multivariate KDE with specified bandwidths.
+    ///
+    /// Use this when you want explicit control over the smoothing parameters.
+    ///
+    /// # Errors
+    ///
+    /// Returns `Error::EmptySamples` if `samples` is empty.
+    /// Returns `Error::DimensionMismatch` if samples have inconsistent dimensions.
+    /// Returns `Error::ZeroDimensions` if samples have zero dimensions.
+    /// Returns `Error::BandwidthDimensionMismatch` if bandwidths length doesn't match dimensions.
+    /// Returns `Error::InvalidBandwidth` if any bandwidth is not positive.
+    pub(crate) fn with_bandwidths(samples: Vec<Vec<f64>>, bandwidths: Vec<f64>) -> Result<Self> {
+        if samples.is_empty() {
+            return Err(Error::EmptySamples);
+        }
+
+        let n_dims = samples[0].len();
+        if n_dims == 0 {
+            return Err(Error::ZeroDimensions);
+        }
+
+        // Check all samples have the same dimensionality
+        for (i, sample) in samples.iter().enumerate() {
+            if sample.len() != n_dims {
+                return Err(Error::DimensionMismatch {
+                    expected: n_dims,
+                    got: sample.len(),
+                    sample_index: i,
+                });
+            }
+        }
+
+        // Check bandwidths length matches dimensions
+        if bandwidths.len() != n_dims {
+            return Err(Error::BandwidthDimensionMismatch {
+                expected: n_dims,
+                got: bandwidths.len(),
+            });
+        }
+
+        // Check all bandwidths are positive
+        for &bw in &bandwidths {
+            if bw <= 0.0 {
+                return Err(Error::InvalidBandwidth(bw));
+            }
+        }
+
+        Ok(Self {
+            samples,
+            bandwidths,
+            n_dims,
+        })
+    }
+
+    /// Computes bandwidths using Scott's rule for multivariate KDE.
+    ///
+    /// Scott's rule for d dimensions: `h_j = n^(-1/(d+4)) * sigma_j`
+    #[allow(clippy::cast_precision_loss)]
+    fn scotts_rule_multivariate(samples: &[Vec<f64>], n_dims: usize) -> Vec<f64> {
+        let n = samples.len() as f64;
+        let d = n_dims as f64;
+
+        // Scott's rule exponent for multivariate: -1/(d+4)
+        let exponent = -1.0 / (d + 4.0);
+        let scale_factor = n.powf(exponent);
+
+        (0..n_dims)
+            .map(|dim| {
+                let std_dev = Self::dimension_std_dev(samples, dim);
+                // For degenerate case where all samples are identical in this dimension,
+                // use a small positive bandwidth
+                if std_dev < f64::EPSILON {
+                    1.0
+                } else {
+                    scale_factor * std_dev
+                }
+            })
+            .collect()
+    }
+
+    /// Computes the sample standard deviation for a single dimension.
+    #[allow(clippy::cast_precision_loss)]
+    fn dimension_std_dev(samples: &[Vec<f64>], dim: usize) -> f64 {
+        let n = samples.len() as f64;
+        let values: Vec<f64> = samples.iter().map(|s| s[dim]).collect();
+        let mean = values.iter().sum::<f64>() / n;
+        let variance = values.iter().map(|x| (x - mean).powi(2)).sum::<f64>() / n;
+        variance.sqrt()
+    }
+
+    /// Returns the number of dimensions.
+    pub(crate) fn n_dims(&self) -> usize {
+        self.n_dims
+    }
+
+    /// Returns the number of samples.
+    #[allow(dead_code)] // Will be used in subsequent stories
+    pub(crate) fn n_samples(&self) -> usize {
+        self.samples.len()
+    }
+
+    /// Returns the bandwidths for each dimension.
+    #[cfg(test)]
+    pub(crate) fn bandwidths(&self) -> &[f64] {
+        &self.bandwidths
+    }
+
+    /// Returns a reference to the samples.
+    #[allow(dead_code)] // Will be used in subsequent stories
+    pub(crate) fn samples(&self) -> &[Vec<f64>] {
+        &self.samples
+    }
+
+    /// Returns the log probability density at point `x`.
+    ///
+    /// This computes the log-density for numerical stability, using the formula:
+    ///
+    /// `log f(x) = log((1/n) * Σ_i Π_j K_hj((x_j - x_ij) / h_j))`
+    ///
+    /// The computation uses the log-sum-exp trick for numerical stability:
+    ///
+    /// `log(Σ exp(a_i)) = max(a) + log(Σ exp(a_i - max(a)))`
+    ///
+    /// # Panics
+    ///
+    /// Panics if `x.len() != self.n_dims`.
+    #[allow(clippy::cast_precision_loss)]
+    pub(crate) fn log_pdf(&self, x: &[f64]) -> f64 {
+        assert_eq!(
+            x.len(),
+            self.n_dims,
+            "Point dimension {} doesn't match KDE dimension {}",
+            x.len(),
+            self.n_dims
+        );
+
+        let n = self.samples.len() as f64;
+
+        // Precompute log normalization constant for each dimension
+        // For a Gaussian kernel: K_h(z) = (1/(h*sqrt(2*pi))) * exp(-0.5*z^2)
+        // log(K_h(z)) = -log(h) - 0.5*log(2*pi) - 0.5*z^2
+        let log_2pi = (2.0 * core::f64::consts::PI).ln();
+        let log_norm_per_dim: Vec<f64> = self
+            .bandwidths
+            .iter()
+            .map(|&h| -h.ln() - 0.5 * log_2pi)
+            .collect();
+
+        // Compute log of kernel contribution for each sample
+        // log(prod_j K_hj(z_j)) = sum_j log(K_hj(z_j))
+        let log_kernels: Vec<f64> = self
+            .samples
+            .iter()
+            .map(|sample| {
+                let mut log_kernel_sum = 0.0;
+                for j in 0..self.n_dims {
+                    let z = (x[j] - sample[j]) / self.bandwidths[j];
+                    log_kernel_sum += log_norm_per_dim[j] - 0.5 * z * z;
+                }
+                log_kernel_sum
+            })
+            .collect();
+
+        // Use log-sum-exp trick for numerical stability
+        // log(sum(exp(log_kernels))) = max + log(sum(exp(log_kernels - max)))
+        let max_log_kernel = log_kernels
+            .iter()
+            .copied()
+            .fold(f64::NEG_INFINITY, f64::max);
+
+        // Handle case where all log_kernels are -inf (extremely unlikely point)
+        if max_log_kernel.is_infinite() && max_log_kernel < 0.0 {
+            return f64::NEG_INFINITY;
+        }
+
+        let sum_exp: f64 = log_kernels
+            .iter()
+            .map(|&lk| (lk - max_log_kernel).exp())
+            .sum();
+
+        // log((1/n) * sum) = -log(n) + log(sum)
+        -n.ln() + max_log_kernel + sum_exp.ln()
+    }
+
+    /// Returns the probability density at point `x`.
+    ///
+    /// The density is computed as the average of multivariate Gaussian kernels
+    /// centered at each sample point:
+    ///
+    /// `f(x) = (1/n) * Σ_i Π_j K_hj((x_j - x_ij) / h_j)`
+    ///
+    /// where `K_hj` is the univariate Gaussian kernel with bandwidth `h_j`.
+    ///
+    /// This method computes in log-space for numerical stability and then
+    /// exponentiates the result.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `x.len() != self.n_dims`.
+    pub(crate) fn pdf(&self, x: &[f64]) -> f64 {
+        self.log_pdf(x).exp()
+    }
+
+    /// Samples a point from the estimated joint density distribution.
+    ///
+    /// Sampling works by:
+    /// 1. Uniformly selecting one of the kernel centers (samples)
+    /// 2. Adding independent Gaussian noise to each dimension with that
+    ///    dimension's bandwidth as the standard deviation
+    ///
+    /// This is equivalent to sampling from a mixture of multivariate Gaussians
+    /// with diagonal covariance matrices, where each mixture component is
+    /// centered at a sample point.
+    ///
+    /// # Returns
+    ///
+    /// A `Vec<f64>` of length `n_dims` representing a sample from the KDE.
+    pub(crate) fn sample<R: Rng>(&self, rng: &mut R) -> Vec<f64> {
+        // Select a random sample to center the kernel on
+        let idx = rng.random_range(0..self.samples.len());
+        let center = &self.samples[idx];
+
+        // Add independent Gaussian noise to each dimension
+        // Using Box-Muller transform for Gaussian sampling
+        center
+            .iter()
+            .zip(self.bandwidths.iter())
+            .map(|(&center_j, &bandwidth_j)| {
+                let u1: f64 = rng.random();
+                let u2: f64 = rng.random();
+
+                // Box-Muller transform: generates standard normal variate
+                let z = (-2.0 * u1.ln()).sqrt() * (2.0 * core::f64::consts::PI * u2).cos();
+
+                // Scale by bandwidth and shift by center
+                center_j + z * bandwidth_j
+            })
+            .collect()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_multivariate_kde_new_basic() {
+        let samples = vec![vec![1.0, 2.0], vec![1.5, 2.5], vec![2.0, 3.0]];
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        assert_eq!(kde.n_dims(), 2);
+        assert_eq!(kde.n_samples(), 3);
+        assert_eq!(kde.bandwidths().len(), 2);
+    }
+
+    #[test]
+    fn test_multivariate_kde_new_single_sample() {
+        let samples = vec![vec![1.0, 2.0, 3.0]];
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        assert_eq!(kde.n_dims(), 3);
+        assert_eq!(kde.n_samples(), 1);
+        // With single sample, bandwidths should default to 1.0 (degenerate case)
+        for &bw in kde.bandwidths() {
+            assert!((bw - 1.0).abs() < f64::EPSILON);
+        }
+    }
+
+    #[test]
+    fn test_multivariate_kde_new_single_dimension() {
+        let samples = vec![vec![1.0], vec![2.0], vec![3.0], vec![4.0], vec![5.0]];
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        assert_eq!(kde.n_dims(), 1);
+        assert_eq!(kde.n_samples(), 5);
+        assert_eq!(kde.bandwidths().len(), 1);
+        // Bandwidth should be positive
+        assert!(kde.bandwidths()[0] > 0.0);
+    }
+
+    #[test]
+    fn test_multivariate_kde_scotts_rule() {
+        // Create samples with known statistics
+        // 10 samples, 2 dimensions
+        let samples: Vec<Vec<f64>> = (0..10)
+            .map(|i| {
+                let x = f64::from(i);
+                vec![x, x * 2.0] // Second dimension has 2x variance
+            })
+            .collect();
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        // Scott's rule: h = n^(-1/(d+4)) * sigma
+        // n=10, d=2: exponent = -1/6 ≈ -0.167
+        // 10^(-1/6) ≈ 0.681
+        // First dim std_dev ≈ 2.87, second ≈ 5.74
+        // Expected bandwidths: ~1.95 and ~3.91
+
+        let bw = kde.bandwidths();
+        assert!(
+            bw[0] > 1.0 && bw[0] < 3.0,
+            "First bandwidth {} unexpected",
+            bw[0]
+        );
+        assert!(
+            bw[1] > 2.0 && bw[1] < 6.0,
+            "Second bandwidth {} unexpected",
+            bw[1]
+        );
+        // Second bandwidth should be approximately 2x the first
+        assert!(
+            (bw[1] / bw[0] - 2.0).abs() < 0.1,
+            "Ratio {} not close to 2",
+            bw[1] / bw[0]
+        );
+    }
+
+    #[test]
+    fn test_multivariate_kde_with_bandwidths() {
+        let samples = vec![vec![1.0, 2.0], vec![3.0, 4.0]];
+        let bandwidths = vec![0.5, 1.0];
+        let kde = MultivariateKDE::with_bandwidths(samples, bandwidths).unwrap();
+
+        assert_eq!(kde.n_dims(), 2);
+        assert!((kde.bandwidths()[0] - 0.5).abs() < f64::EPSILON);
+        assert!((kde.bandwidths()[1] - 1.0).abs() < f64::EPSILON);
+    }
+
+    #[test]
+    fn test_multivariate_kde_empty_samples() {
+        let samples: Vec<Vec<f64>> = vec![];
+        let result = MultivariateKDE::new(samples);
+        assert!(matches!(result, Err(Error::EmptySamples)));
+    }
+
+    #[test]
+    fn test_multivariate_kde_zero_dimensions() {
+        let samples = vec![vec![], vec![]];
+        let result = MultivariateKDE::new(samples);
+        assert!(matches!(result, Err(Error::ZeroDimensions)));
+    }
+
+    #[test]
+    fn test_multivariate_kde_dimension_mismatch() {
+        let samples = vec![vec![1.0, 2.0], vec![3.0]]; // Second sample has wrong dimensions
+        let result = MultivariateKDE::new(samples);
+        assert!(matches!(
+            result,
+            Err(Error::DimensionMismatch {
+                expected: 2,
+                got: 1,
+                sample_index: 1
+            })
+        ));
+    }
+
+    #[test]
+    fn test_multivariate_kde_with_bandwidths_wrong_length() {
+        let samples = vec![vec![1.0, 2.0], vec![3.0, 4.0]];
+        let bandwidths = vec![0.5]; // Only 1 bandwidth for 2 dimensions
+        let result = MultivariateKDE::with_bandwidths(samples, bandwidths);
+        assert!(matches!(
+            result,
+            Err(Error::BandwidthDimensionMismatch {
+                expected: 2,
+                got: 1
+            })
+        ));
+    }
+
+    #[test]
+    fn test_multivariate_kde_with_bandwidths_zero() {
+        let samples = vec![vec![1.0, 2.0], vec![3.0, 4.0]];
+        let bandwidths = vec![0.5, 0.0]; // Second bandwidth is zero
+        let result = MultivariateKDE::with_bandwidths(samples, bandwidths);
+        assert!(matches!(result, Err(Error::InvalidBandwidth(bw)) if bw == 0.0));
+    }
+
+    #[test]
+    fn test_multivariate_kde_with_bandwidths_negative() {
+        let samples = vec![vec![1.0, 2.0], vec![3.0, 4.0]];
+        let bandwidths = vec![0.5, -1.0]; // Negative bandwidth
+        let result = MultivariateKDE::with_bandwidths(samples, bandwidths);
+        assert!(
+            matches!(result, Err(Error::InvalidBandwidth(bw)) if (bw - (-1.0)).abs() < f64::EPSILON)
+        );
+    }
+
+    #[test]
+    fn test_multivariate_kde_identical_samples() {
+        // All samples identical - should handle degenerate case
+        let samples = vec![vec![5.0, 10.0], vec![5.0, 10.0], vec![5.0, 10.0]];
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        // Bandwidths should default to 1.0 for degenerate dimensions
+        for &bw in kde.bandwidths() {
+            assert!((bw - 1.0).abs() < f64::EPSILON);
+        }
+    }
+
+    #[test]
+    fn test_multivariate_kde_high_dimensional() {
+        // Test with higher dimensions
+        let samples: Vec<Vec<f64>> = (0..20)
+            .map(|i| {
+                let x = f64::from(i);
+                vec![x, x * 0.5, x * 2.0, x * 0.1, x * 10.0]
+            })
+            .collect();
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        assert_eq!(kde.n_dims(), 5);
+        assert_eq!(kde.n_samples(), 20);
+        assert_eq!(kde.bandwidths().len(), 5);
+
+        // All bandwidths should be positive
+        for &bw in kde.bandwidths() {
+            assert!(bw > 0.0);
+        }
+    }
+
+    #[test]
+    fn test_multivariate_kde_samples_accessor() {
+        let samples = vec![vec![1.0, 2.0], vec![3.0, 4.0]];
+        let kde = MultivariateKDE::new(samples.clone()).unwrap();
+
+        assert_eq!(kde.samples(), &samples);
+    }
+
+    // ==================== PDF Tests ====================
+
+    #[test]
+    fn test_multivariate_kde_pdf_basic() {
+        let samples = vec![vec![0.0, 0.0], vec![1.0, 1.0], vec![2.0, 2.0]];
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        // Density should be positive everywhere
+        assert!(kde.pdf(&[0.0, 0.0]) > 0.0);
+        assert!(kde.pdf(&[1.0, 1.0]) > 0.0);
+        assert!(kde.pdf(&[2.0, 2.0]) > 0.0);
+        assert!(kde.pdf(&[0.5, 0.5]) > 0.0);
+
+        // Density should be higher near sample points
+        let near_density = kde.pdf(&[1.0, 1.0]);
+        let far_density = kde.pdf(&[10.0, 10.0]);
+        assert!(near_density > far_density);
+    }
+
+    #[test]
+    fn test_multivariate_kde_pdf_with_custom_bandwidths() {
+        let samples = vec![vec![0.0, 0.0], vec![1.0, 1.0]];
+        let bandwidths = vec![0.5, 0.5];
+        let kde = MultivariateKDE::with_bandwidths(samples, bandwidths).unwrap();
+
+        // Density should be positive
+        assert!(kde.pdf(&[0.5, 0.5]) > 0.0);
+        assert!(kde.pdf(&[0.0, 0.0]) > 0.0);
+    }
+
+    #[test]
+    fn test_multivariate_kde_pdf_single_sample() {
+        let samples = vec![vec![5.0, 10.0]];
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        // Should have positive density near the sample
+        assert!(kde.pdf(&[5.0, 10.0]) > 0.0);
+        assert!(kde.pdf(&[4.5, 9.5]) > 0.0);
+    }
+
+    #[test]
+    fn test_multivariate_kde_log_pdf_consistency() {
+        let samples = vec![vec![0.0, 0.0], vec![1.0, 1.0], vec![2.0, 2.0]];
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        // log_pdf and pdf should be consistent: exp(log_pdf(x)) == pdf(x)
+        let test_points = vec![
+            vec![0.0, 0.0],
+            vec![1.0, 1.0],
+            vec![0.5, 0.5],
+            vec![3.0, 3.0],
+        ];
+
+        for point in test_points {
+            let log_p = kde.log_pdf(&point);
+            let p = kde.pdf(&point);
+            let p_from_log = log_p.exp();
+            assert!(
+                (p - p_from_log).abs() < 1e-10,
+                "pdf={p}, exp(log_pdf)={p_from_log}"
+            );
+        }
+    }
+
+    #[test]
+    fn test_multivariate_kde_pdf_integrates_to_one_1d() {
+        // Test with 1D case first (should match univariate KDE behavior)
+        let samples = vec![vec![0.0], vec![1.0], vec![2.0], vec![3.0], vec![4.0]];
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        // Numerical integration over a wide range
+        let n_points = 1000;
+        let low = -10.0;
+        let high = 15.0;
+        let dx = (high - low) / f64::from(n_points);
+
+        let integral: f64 = (0..n_points)
+            .map(|i| {
+                let x = low + (f64::from(i) + 0.5) * dx;
+                kde.pdf(&[x]) * dx
+            })
+            .sum();
+
+        // Should be approximately 1.0 (within numerical error)
+        assert!(
+            (integral - 1.0).abs() < 0.02,
+            "1D integral = {integral}, expected ~1.0"
+        );
+    }
+
+    #[test]
+    fn test_multivariate_kde_pdf_integrates_to_one_2d() {
+        // Test with 2D case
+        let samples = vec![
+            vec![0.0, 0.0],
+            vec![1.0, 0.0],
+            vec![0.0, 1.0],
+            vec![1.0, 1.0],
+            vec![0.5, 0.5],
+        ];
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        // Numerical integration over a 2D grid
+        let n_points = 100; // 100x100 = 10000 points
+        let low = -5.0;
+        let high = 6.0;
+        let dx = (high - low) / f64::from(n_points);
+
+        let mut integral = 0.0;
+        for i in 0..n_points {
+            for j in 0..n_points {
+                let x = low + (f64::from(i) + 0.5) * dx;
+                let y = low + (f64::from(j) + 0.5) * dx;
+                integral += kde.pdf(&[x, y]) * dx * dx;
+            }
+        }
+
+        // Should be approximately 1.0 (within numerical error)
+        // 2D integration has more error, so use larger tolerance
+        assert!(
+            (integral - 1.0).abs() < 0.05,
+            "2D integral = {integral}, expected ~1.0"
+        );
+    }
+
+    #[test]
+    fn test_multivariate_kde_pdf_symmetry() {
+        // With symmetric samples, PDF should be symmetric
+        let samples = vec![
+            vec![1.0, 0.0],
+            vec![-1.0, 0.0],
+            vec![0.0, 1.0],
+            vec![0.0, -1.0],
+        ];
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        // Density at symmetric points should be equal
+        let d1 = kde.pdf(&[0.5, 0.0]);
+        let d2 = kde.pdf(&[-0.5, 0.0]);
+        assert!(
+            (d1 - d2).abs() < 1e-10,
+            "Symmetric points have different densities: {d1} vs {d2}"
+        );
+
+        let d3 = kde.pdf(&[0.0, 0.5]);
+        let d4 = kde.pdf(&[0.0, -0.5]);
+        assert!(
+            (d3 - d4).abs() < 1e-10,
+            "Symmetric points have different densities: {d3} vs {d4}"
+        );
+    }
+
+    #[test]
+    fn test_multivariate_kde_pdf_high_dimensional() {
+        // Test with higher dimensions
+        let samples: Vec<Vec<f64>> = (0..10)
+            .map(|i| {
+                let x = f64::from(i) * 0.1;
+                vec![x, x, x, x, x] // 5D
+            })
+            .collect();
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        // Density should be positive
+        assert!(kde.pdf(&[0.5, 0.5, 0.5, 0.5, 0.5]) > 0.0);
+        assert!(kde.pdf(&[0.0, 0.0, 0.0, 0.0, 0.0]) > 0.0);
+
+        // Log PDF should be finite
+        let log_p = kde.log_pdf(&[0.5, 0.5, 0.5, 0.5, 0.5]);
+        assert!(log_p.is_finite());
+    }
+
+    #[test]
+    fn test_multivariate_kde_pdf_numerical_stability() {
+        // Test numerical stability with points far from samples
+        let samples = vec![vec![0.0, 0.0], vec![1.0, 1.0]];
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        // Very far point should have very small but non-negative density
+        let far_pdf = kde.pdf(&[100.0, 100.0]);
+        assert!(far_pdf >= 0.0);
+        assert!(far_pdf.is_finite() || far_pdf == 0.0);
+
+        // Log PDF should be finite (or -inf for zero density)
+        let far_log_pdf = kde.log_pdf(&[100.0, 100.0]);
+        assert!(far_log_pdf.is_finite() || far_log_pdf.is_infinite());
+    }
+
+    #[test]
+    #[should_panic(expected = "Point dimension")]
+    fn test_multivariate_kde_pdf_wrong_dimension() {
+        let samples = vec![vec![0.0, 0.0], vec![1.0, 1.0]];
+        let kde = MultivariateKDE::new(samples).unwrap();
+
+        // Should panic with wrong dimension
+        let _ = kde.pdf(&[0.0]); // Only 1 value for 2D KDE
+    }
+
+    // ==================== Sampling Tests ====================
+
+    #[test]
+    fn test_multivariate_kde_sample_basic() {
+        let samples = vec![vec![0.0, 0.0], vec![1.0, 1.0], vec![2.0, 2.0]];
+        let kde = MultivariateKDE::new(samples).unwrap();
+        let mut rng = rand::rng();
+
+        // Sample should have correct dimensionality
+        let sample = kde.sample(&mut rng);
+        assert_eq!(sample.len(), 2);
+    }
+
+    #[test]
+    fn test_multivariate_kde_sample_in_reasonable_range() {
+        let samples = vec![
+            vec![0.0, 0.0],
+            vec![1.0, 1.0],
+            vec![2.0, 2.0],
+            vec![3.0, 3.0],
+            vec![4.0, 4.0],
+        ];
+        let kde = MultivariateKDE::new(samples).unwrap();
+        let mut rng = rand::rng();
+
+        // Samples should generally be in a reasonable range around the data
+        for _ in 0..100 {
+            let s = kde.sample(&mut rng);
+            // With high probability, samples should be within a few bandwidths
+            // of the data range. Use a generous range to avoid flaky tests.
+            assert!(
+                s[0] > -10.0 && s[0] < 15.0,
+                "Sample dimension 0: {} outside expected range",
+                s[0]
+            );
+            assert!(
+                s[1] > -10.0 && s[1] < 15.0,
+                "Sample dimension 1: {} outside expected range",
+                s[1]
+            );
+        }
+    }
+
+    #[test]
+    fn test_multivariate_kde_sample_single_sample() {
+        // When KDE has only one sample, all samples should be centered around it
+        let samples = vec![vec![5.0, 10.0]];
+        let kde = MultivariateKDE::new(samples).unwrap();
+        let mut rng = rand::rng();
+
+        // Generate many samples and check they cluster around (5.0, 10.0)
+        let n_samples = 100;
+        let mut sum_x = 0.0;
+        let mut sum_y = 0.0;
+        for _ in 0..n_samples {
+            let s = kde.sample(&mut rng);
+            sum_x += s[0];
+            sum_y += s[1];
+        }
+
+        let mean_x = sum_x / f64::from(n_samples);
+        let mean_y = sum_y / f64::from(n_samples);
+
+        // Mean should be close to the single sample point
+        // With 100 samples and bandwidth=1.0, we expect mean within ~0.3 of center
+        assert!(
+            (mean_x - 5.0).abs() < 1.0,
+            "Mean x={mean_x}, expected close to 5.0"
+        );
+        assert!(
+            (mean_y - 10.0).abs() < 1.0,
+            "Mean y={mean_y}, expected close to 10.0"
+        );
+    }
+
+    #[test]
+    fn test_multivariate_kde_sample_high_dimensional() {
+        // Test sampling in higher dimensions
+        let samples: Vec<Vec<f64>> = (0..10)
+            .map(|i| {
+                let x = f64::from(i) * 0.5;
+                vec![x, x * 2.0, x * 0.5, x + 1.0, x - 1.0] // 5D
+            })
+            .collect();
+        let kde = MultivariateKDE::new(samples).unwrap();
+        let mut rng = rand::rng();
+
+        // Sample should have correct dimensionality
+        for _ in 0..50 {
+            let sample = kde.sample(&mut rng);
+            assert_eq!(sample.len(), 5);
+            // All values should be finite
+            for &val in &sample {
+                assert!(val.is_finite(), "Sample value is not finite: {val}");
+            }
+        }
+    }
+
+    #[test]
+    #[allow(clippy::cast_precision_loss)]
+    fn test_multivariate_kde_sample_respects_bandwidth() {
+        // Create samples all at origin with large custom bandwidth
+        let data = vec![vec![0.0, 0.0], vec![0.0, 0.0], vec![0.0, 0.0]];
+        let bandwidths = vec![0.1, 10.0]; // Small bandwidth in x, large in y
+        let kde = MultivariateKDE::with_bandwidths(data, bandwidths).unwrap();
+        let mut rng = rand::rng();
+
+        // Generate samples and check variance in each dimension
+        let n_samples = 1000;
+        let mut values_x: Vec<f64> = Vec::with_capacity(n_samples);
+        let mut values_y: Vec<f64> = Vec::with_capacity(n_samples);
+
+        for _ in 0..n_samples {
+            let s = kde.sample(&mut rng);
+            values_x.push(s[0]);
+            values_y.push(s[1]);
+        }
+
+        // Compute sample variances
+        let n = n_samples as f64;
+        let mean_x: f64 = values_x.iter().sum::<f64>() / n;
+        let mean_y: f64 = values_y.iter().sum::<f64>() / n;
+
+        let var_x: f64 = values_x.iter().map(|x| (x - mean_x).powi(2)).sum::<f64>() / n;
+        let var_y: f64 = values_y.iter().map(|y| (y - mean_y).powi(2)).sum::<f64>() / n;
+
+        // Variance should be approximately bandwidth^2
+        // x: bandwidth=0.1, expected variance ~0.01
+        // y: bandwidth=10.0, expected variance ~100.0
+        assert!(
+            var_x < 0.05,
+            "X variance {var_x} too large for bandwidth 0.1"
+        );
+        assert!(
+            var_y > 50.0 && var_y < 200.0,
+            "Y variance {var_y} unexpected for bandwidth 10.0"
+        );
+    }
+
+    #[test]
+    fn test_multivariate_kde_sample_distribution_shape() {
+        // Create samples along a diagonal line
+        let data = vec![
+            vec![0.0, 0.0],
+            vec![1.0, 1.0],
+            vec![2.0, 2.0],
+            vec![3.0, 3.0],
+            vec![4.0, 4.0],
+        ];
+        let kde = MultivariateKDE::new(data).unwrap();
+        let mut rng = rand::rng();
+
+        // Sample many points and verify the mean is near the center
+        let n_samples = 500;
+        let mut sum = [0.0, 0.0];
+
+        for _ in 0..n_samples {
+            let s = kde.sample(&mut rng);
+            sum[0] += s[0];
+            sum[1] += s[1];
+        }
+
+        let mean_x = sum[0] / f64::from(n_samples);
+        let mean_y = sum[1] / f64::from(n_samples);
+
+        // Mean should be close to (2.0, 2.0) - the center of the samples
+        assert!(
+            (mean_x - 2.0).abs() < 0.5,
+            "Mean x={mean_x}, expected close to 2.0"
+        );
+        assert!(
+            (mean_y - 2.0).abs() < 0.5,
+            "Mean y={mean_y}, expected close to 2.0"
+        );
+    }
+
+    #[test]
+    fn test_multivariate_kde_sample_deterministic_with_seeded_rng() {
+        use rand::SeedableRng;
+
+        let data = vec![vec![1.0, 2.0], vec![3.0, 4.0]];
+        let kde = MultivariateKDE::new(data).unwrap();
+
+        // Use a seeded RNG for reproducibility
+        let mut rng1 = rand::rngs::StdRng::seed_from_u64(42);
+        let mut rng2 = rand::rngs::StdRng::seed_from_u64(42);
+
+        // Same seed should produce same samples
+        let result1 = kde.sample(&mut rng1);
+        let result2 = kde.sample(&mut rng2);
+
+        assert!(
+            (result1[0] - result2[0]).abs() < f64::EPSILON,
+            "Samples with same seed differ in dimension 0"
+        );
+        assert!(
+            (result1[1] - result2[1]).abs() < f64::EPSILON,
+            "Samples with same seed differ in dimension 1"
+        );
+    }
+}

src/kde/univariate.rs

@@ -5,7 +5,7 @@
 
 use rand::Rng;
 
-use crate::error::{Result, TpeError};
+use crate::error::{Error, Result};
 
 /// A Gaussian kernel density estimator for continuous distributions.
 ///
@@ -45,10 +45,10 @@ impl KernelDensityEstimator {
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::EmptySamples` if `samples` is empty.
+    /// Returns `Error::EmptySamples` if `samples` is empty.
     pub(crate) fn new(samples: Vec<f64>) -> Result<Self> {
         if samples.is_empty() {
-            return Err(TpeError::EmptySamples);
+            return Err(Error::EmptySamples);
         }
 
         let bandwidth = Self::scotts_rule(&samples);
@@ -61,14 +61,14 @@ impl KernelDensityEstimator {
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::EmptySamples` if `samples` is empty.
-    /// Returns `TpeError::InvalidBandwidth` if `bandwidth` is not positive.
+    /// Returns `Error::EmptySamples` if `samples` is empty.
+    /// Returns `Error::InvalidBandwidth` if `bandwidth` is not positive.
     pub(crate) fn with_bandwidth(samples: Vec<f64>, bandwidth: f64) -> Result<Self> {
         if samples.is_empty() {
-            return Err(TpeError::EmptySamples);
+            return Err(Error::EmptySamples);
         }
         if bandwidth <= 0.0 {
-            return Err(TpeError::InvalidBandwidth(bandwidth));
+            return Err(Error::InvalidBandwidth(bandwidth));
         }
 
         Ok(Self { samples, bandwidth })
@@ -261,20 +261,20 @@ mod tests {
     fn test_kde_empty_samples() {
         let samples: Vec<f64> = vec![];
         let result = KernelDensityEstimator::new(samples);
-        assert!(matches!(result, Err(TpeError::EmptySamples)));
+        assert!(matches!(result, Err(Error::EmptySamples)));
     }
 
     #[test]
     fn test_kde_zero_bandwidth() {
         let samples = vec![1.0, 2.0, 3.0];
         let result = KernelDensityEstimator::with_bandwidth(samples, 0.0);
-        assert!(matches!(result, Err(TpeError::InvalidBandwidth(_))));
+        assert!(matches!(result, Err(Error::InvalidBandwidth(_))));
     }
 
     #[test]
     fn test_kde_negative_bandwidth() {
         let samples = vec![1.0, 2.0, 3.0];
         let result = KernelDensityEstimator::with_bandwidth(samples, -1.0);
-        assert!(matches!(result, Err(TpeError::InvalidBandwidth(_))));
+        assert!(matches!(result, Err(Error::InvalidBandwidth(_))));
     }
 }

src/lib.rs

@@ -9,10 +9,16 @@
 #![deny(clippy::pedantic)]
 #![deny(clippy::std_instead_of_core)]
 
-//! A Tree-Parzen Estimator (TPE) library for black-box optimization.
+//! A black-box optimization library with multiple sampling strategies.
 //!
 //! This library provides an Optuna-like API for hyperparameter optimization
-//! using the Tree-Parzen Estimator algorithm. It supports:
+//! with support for multiple sampling algorithms:
+//!
+//! - **Random Search** - Simple random sampling for baseline comparisons
+//! - **TPE (Tree-Parzen Estimator)** - Bayesian optimization for efficient search
+//! - **Grid Search** - Exhaustive search over a specified parameter grid
+//!
+//! Additional features include:
 //!
 //! - Float, integer, and categorical parameter types
 //! - Log-scale and stepped parameter sampling
@@ -33,7 +39,7 @@
 //! study
 //!     .optimize_with_sampler(20, |trial| {
 //!         let x = trial.suggest_float("x", -10.0, 10.0)?;
-//!         Ok::<_, optimizer::TpeError>(x * x)
+//!         Ok::<_, optimizer::Error>(x * x)
 //!     })
 //!     .unwrap();
 //!
@@ -86,14 +92,27 @@
 //!         let optimizer = trial.suggest_categorical("optimizer", &["sgd", "adam", "rmsprop"])?;
 //!
 //!         // Return objective value
-//!         Ok::<_, optimizer::TpeError>(x * n as f64)
+//!         Ok::<_, optimizer::Error>(x * n as f64)
 //!     })
 //!     .unwrap();
 //! ```
 //!
-//! # Configuring TPE
+//! # Available Samplers
 //!
-//! The [`sampler::tpe::TpeSampler`] can be configured using the builder pattern:
+//! ## Random Search
+//!
+//! The simplest sampling strategy, useful for baselines:
+//!
+//! ```
+//! use optimizer::sampler::random::RandomSampler;
+//! use optimizer::{Direction, Study};
+//!
+//! let study: Study<f64> = Study::with_sampler(Direction::Minimize, RandomSampler::with_seed(42));
+//! ```
+//!
+//! ## TPE (Tree-Parzen Estimator)
+//!
+//! Bayesian optimization that learns from previous trials:
 //!
 //! ```
 //! use optimizer::sampler::tpe::TpeSampler;
@@ -107,6 +126,21 @@
 //!     .unwrap();
 //! ```
 //!
+//! ## Grid Search
+//!
+//! Exhaustive search over a discretized parameter space:
+//!
+//! ```
+//! use optimizer::sampler::grid::GridSearchSampler;
+//! use optimizer::{Direction, Study};
+//!
+//! let sampler = GridSearchSampler::builder()
+//!     .n_points_per_param(10)  // Points per parameter dimension
+//!     .build();
+//!
+//! let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+//! ```
+//!
 //! # Async and Parallel Optimization
 //!
 //! With the `async` feature enabled, you can run trials asynchronously:
@@ -140,8 +174,8 @@ mod study;
 mod trial;
 mod types;
 
-pub use error::{Result, TpeError};
+pub use error::{Error, Result};
 pub use param::ParamValue;
 pub use study::Study;
-pub use trial::Trial;
+pub use trial::{SuggestableRange, Trial};
 pub use types::{Direction, TrialState};

src/sampler/mod.rs

@@ -1,10 +1,16 @@
 //! Sampler trait and implementations for parameter sampling.
 
+pub mod grid;
+pub mod multivariate_tpe;
 pub mod random;
 pub mod tpe;
 
 use std::collections::HashMap;
 
+pub use multivariate_tpe::{
+    ConstantLiarStrategy, MultivariateTpeSampler, MultivariateTpeSamplerBuilder,
+};
+
 use crate::distribution::Distribution;
 use crate::param::ParamValue;
 
@@ -42,6 +48,57 @@ impl<V> CompletedTrial<V> {
     }
 }
 
+/// A pending (running) trial with its parameters and distributions, but no objective value yet.
+///
+/// This struct represents a trial that has been started and has sampled parameters,
+/// but is still running and hasn't returned an objective value. It is used with the
+/// constant liar strategy for parallel optimization.
+///
+/// # Examples
+///
+/// ```ignore
+/// use std::collections::HashMap;
+/// use optimizer::sampler::PendingTrial;
+/// use optimizer::param::ParamValue;
+/// use optimizer::distribution::{Distribution, FloatDistribution};
+///
+/// let mut params = HashMap::new();
+/// params.insert("x".to_string(), ParamValue::Float(0.5));
+///
+/// let mut distributions = HashMap::new();
+/// distributions.insert("x".to_string(), Distribution::Float(FloatDistribution {
+///     low: 0.0, high: 1.0, log_scale: false, step: None,
+/// }));
+///
+/// let pending = PendingTrial::new(1, params, distributions);
+/// assert_eq!(pending.id, 1);
+/// ```
+#[derive(Clone, Debug)]
+pub struct PendingTrial {
+    /// The unique identifier for this trial.
+    pub id: u64,
+    /// The sampled parameter values, keyed by parameter name.
+    pub params: HashMap<String, ParamValue>,
+    /// The parameter distributions used, keyed by parameter name.
+    pub distributions: HashMap<String, Distribution>,
+}
+
+impl PendingTrial {
+    /// Creates a new pending trial.
+    #[must_use]
+    pub fn new(
+        id: u64,
+        params: HashMap<String, ParamValue>,
+        distributions: HashMap<String, Distribution>,
+    ) -> Self {
+        Self {
+            id,
+            params,
+            distributions,
+        }
+    }
+}
+
 /// Trait for pluggable parameter sampling strategies.
 ///
 /// Samplers are responsible for generating parameter values based on

src/sampler/tpe/gamma.rs

@@ -0,0 +1,670 @@
+use core::fmt::Debug;
+
+use crate::Error;
+
+/// A strategy for computing the gamma quantile in TPE.
+///
+/// The gamma value determines what fraction of trials are considered "good"
+/// when splitting the trial history. Different strategies can adapt this
+/// fraction based on the number of completed trials.
+///
+/// # Implementation Notes
+///
+/// - The returned gamma must be in the range (0.0, 1.0)
+/// - Implementations should be deterministic for reproducibility
+/// - The `clone_box` method enables trait object cloning
+///
+/// # Examples
+///
+/// ```
+/// use optimizer::sampler::tpe::GammaStrategy;
+///
+/// #[derive(Debug, Clone)]
+/// struct ConstantGamma(f64);
+///
+/// impl GammaStrategy for ConstantGamma {
+///     fn gamma(&self, _n_trials: usize) -> f64 {
+///         self.0
+///     }
+///
+///     fn clone_box(&self) -> Box<dyn GammaStrategy> {
+///         Box::new(self.clone())
+///     }
+/// }
+/// ```
+pub trait GammaStrategy: Send + Sync + Debug {
+    /// Computes the gamma quantile based on the number of completed trials.
+    ///
+    /// # Arguments
+    ///
+    /// * `n_trials` - The number of completed trials in the history.
+    ///
+    /// # Returns
+    ///
+    /// A gamma value in the range (0.0, 1.0). Values outside this range
+    /// will be clamped by the sampler.
+    fn gamma(&self, n_trials: usize) -> f64;
+
+    /// Creates a boxed clone of this strategy.
+    ///
+    /// This method enables cloning of trait objects, which is necessary
+    /// for the builder pattern and sampler configuration.
+    fn clone_box(&self) -> Box<dyn GammaStrategy>;
+}
+
+impl Clone for Box<dyn GammaStrategy> {
+    fn clone(&self) -> Self {
+        self.clone_box()
+    }
+}
+
+/// A fixed gamma strategy that returns a constant value.
+///
+/// This is the simplest strategy and the default behavior of TPE.
+/// The gamma value remains constant regardless of the number of trials.
+///
+/// # Examples
+///
+/// ```
+/// use optimizer::sampler::tpe::{FixedGamma, TpeSampler};
+///
+/// // Use 15% of trials as "good"
+/// let sampler = TpeSampler::builder()
+///     .gamma_strategy(FixedGamma::new(0.15).unwrap())
+///     .build()
+///     .unwrap();
+/// ```
+#[derive(Debug, Clone, Copy)]
+pub struct FixedGamma {
+    gamma: f64,
+}
+
+impl FixedGamma {
+    /// Creates a new fixed gamma strategy.
+    ///
+    /// # Arguments
+    ///
+    /// * `gamma` - The constant gamma value to use.
+    ///
+    /// # Errors
+    ///
+    /// Returns `Error::InvalidGamma` if gamma is not in (0.0, 1.0).
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use optimizer::sampler::tpe::FixedGamma;
+    ///
+    /// let strategy = FixedGamma::new(0.25).unwrap();
+    /// assert!((strategy.value() - 0.25).abs() < f64::EPSILON);
+    /// ```
+    pub fn new(gamma: f64) -> crate::Result<Self> {
+        if gamma <= 0.0 || gamma >= 1.0 {
+            return Err(Error::InvalidGamma(gamma));
+        }
+        Ok(Self { gamma })
+    }
+
+    /// Returns the fixed gamma value.
+    #[must_use]
+    pub fn value(&self) -> f64 {
+        self.gamma
+    }
+}
+
+impl Default for FixedGamma {
+    /// Creates a fixed gamma strategy with the default value of 0.25.
+    fn default() -> Self {
+        Self { gamma: 0.25 }
+    }
+}
+
+impl GammaStrategy for FixedGamma {
+    fn gamma(&self, _n_trials: usize) -> f64 {
+        self.gamma
+    }
+
+    fn clone_box(&self) -> Box<dyn GammaStrategy> {
+        Box::new(*self)
+    }
+}
+
+/// A linear gamma strategy that interpolates between min and max values.
+///
+/// The gamma value increases linearly from `gamma_min` to `gamma_max` as the
+/// number of trials grows from 0 to `n_trials_max`. Beyond `n_trials_max`,
+/// gamma remains at `gamma_max`.
+///
+/// This strategy is useful when you want to be more explorative early on
+/// (smaller gamma = fewer "good" trials) and more exploitative later
+/// (larger gamma = more "good" trials).
+///
+/// # Formula
+///
+/// ```text
+/// gamma = gamma_min + (gamma_max - gamma_min) * min(n_trials / n_trials_max, 1.0)
+/// ```
+///
+/// # Examples
+///
+/// ```
+/// use optimizer::sampler::tpe::{GammaStrategy, LinearGamma, TpeSampler};
+///
+/// let strategy = LinearGamma::new(0.1, 0.4, 100).unwrap();
+///
+/// // At 0 trials: gamma = 0.1
+/// assert!((strategy.gamma(0) - 0.1).abs() < f64::EPSILON);
+///
+/// // At 50 trials: gamma = 0.25 (midpoint)
+/// assert!((strategy.gamma(50) - 0.25).abs() < f64::EPSILON);
+///
+/// // At 100+ trials: gamma = 0.4
+/// assert!((strategy.gamma(100) - 0.4).abs() < f64::EPSILON);
+/// assert!((strategy.gamma(200) - 0.4).abs() < f64::EPSILON);
+/// ```
+#[derive(Debug, Clone, Copy)]
+pub struct LinearGamma {
+    gamma_min: f64,
+    gamma_max: f64,
+    n_trials_max: usize,
+}
+
+impl LinearGamma {
+    /// Creates a new linear gamma strategy.
+    ///
+    /// # Arguments
+    ///
+    /// * `gamma_min` - The minimum gamma value (at 0 trials).
+    /// * `gamma_max` - The maximum gamma value (at `n_trials_max` trials).
+    /// * `n_trials_max` - The number of trials at which gamma reaches its maximum.
+    ///
+    /// # Errors
+    ///
+    /// Returns `Error::InvalidGamma` if:
+    /// - `gamma_min` is not in (0.0, 1.0)
+    /// - `gamma_max` is not in (0.0, 1.0)
+    /// - `gamma_min > gamma_max`
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use optimizer::sampler::tpe::LinearGamma;
+    ///
+    /// // Gamma goes from 0.1 to 0.3 over 50 trials
+    /// let strategy = LinearGamma::new(0.1, 0.3, 50).unwrap();
+    /// ```
+    pub fn new(gamma_min: f64, gamma_max: f64, n_trials_max: usize) -> crate::Result<Self> {
+        if gamma_min <= 0.0 || gamma_min >= 1.0 {
+            return Err(Error::InvalidGamma(gamma_min));
+        }
+        if gamma_max <= 0.0 || gamma_max >= 1.0 {
+            return Err(Error::InvalidGamma(gamma_max));
+        }
+        if gamma_min > gamma_max {
+            return Err(Error::InvalidGamma(gamma_min));
+        }
+        Ok(Self {
+            gamma_min,
+            gamma_max,
+            n_trials_max,
+        })
+    }
+
+    /// Returns the minimum gamma value.
+    #[must_use]
+    pub fn gamma_min(&self) -> f64 {
+        self.gamma_min
+    }
+
+    /// Returns the maximum gamma value.
+    #[must_use]
+    pub fn gamma_max(&self) -> f64 {
+        self.gamma_max
+    }
+
+    /// Returns the number of trials at which gamma reaches its maximum.
+    #[must_use]
+    pub fn n_trials_max(&self) -> usize {
+        self.n_trials_max
+    }
+}
+
+impl Default for LinearGamma {
+    /// Creates a linear gamma strategy with default values:
+    /// - `gamma_min`: 0.10
+    /// - `gamma_max`: 0.25
+    /// - `n_trials_max`: 100
+    fn default() -> Self {
+        Self {
+            gamma_min: 0.10,
+            gamma_max: 0.25,
+            n_trials_max: 100,
+        }
+    }
+}
+
+impl GammaStrategy for LinearGamma {
+    #[allow(clippy::cast_precision_loss)]
+    fn gamma(&self, n_trials: usize) -> f64 {
+        if self.n_trials_max == 0 {
+            return self.gamma_max;
+        }
+        let t = (n_trials as f64 / self.n_trials_max as f64).min(1.0);
+        self.gamma_min + (self.gamma_max - self.gamma_min) * t
+    }
+
+    fn clone_box(&self) -> Box<dyn GammaStrategy> {
+        Box::new(*self)
+    }
+}
+
+/// A square root gamma strategy inspired by Optuna's default behavior.
+///
+/// The gamma value is computed based on the inverse square root of the number
+/// of trials, providing a balance between exploration and exploitation that
+/// naturally adapts as more data becomes available.
+///
+/// # Formula
+///
+/// ```text
+/// n_good = max(1, floor(gamma_factor / sqrt(n_trials)))
+/// gamma = min(gamma_max, n_good / n_trials)
+/// ```
+///
+/// When `n_trials` is 0, returns `gamma_max`.
+///
+/// # Examples
+///
+/// ```
+/// use optimizer::sampler::tpe::{GammaStrategy, SqrtGamma, TpeSampler};
+///
+/// let strategy = SqrtGamma::default();
+///
+/// // Gamma decreases as trials increase
+/// let g10 = strategy.gamma(10);
+/// let g100 = strategy.gamma(100);
+/// assert!(g10 > g100, "Gamma should decrease with more trials");
+/// ```
+#[derive(Debug, Clone, Copy)]
+pub struct SqrtGamma {
+    gamma_factor: f64,
+    gamma_max: f64,
+}
+
+impl SqrtGamma {
+    /// Creates a new square root gamma strategy.
+    ///
+    /// # Arguments
+    ///
+    /// * `gamma_factor` - The factor controlling how quickly gamma decreases.
+    ///   Higher values mean more "good" trials at any given point.
+    /// * `gamma_max` - The maximum gamma value (used when `n_trials` is small).
+    ///
+    /// # Errors
+    ///
+    /// Returns `Error::InvalidGamma` if:
+    /// - `gamma_factor` is not positive
+    /// - `gamma_max` is not in (0.0, 1.0)
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use optimizer::sampler::tpe::SqrtGamma;
+    ///
+    /// let strategy = SqrtGamma::new(1.0, 0.25).unwrap();
+    /// ```
+    pub fn new(gamma_factor: f64, gamma_max: f64) -> crate::Result<Self> {
+        if gamma_factor <= 0.0 {
+            return Err(Error::InvalidGamma(gamma_factor));
+        }
+        if gamma_max <= 0.0 || gamma_max >= 1.0 {
+            return Err(Error::InvalidGamma(gamma_max));
+        }
+        Ok(Self {
+            gamma_factor,
+            gamma_max,
+        })
+    }
+
+    /// Returns the gamma factor.
+    #[must_use]
+    pub fn gamma_factor(&self) -> f64 {
+        self.gamma_factor
+    }
+
+    /// Returns the maximum gamma value.
+    #[must_use]
+    pub fn gamma_max(&self) -> f64 {
+        self.gamma_max
+    }
+}
+
+impl Default for SqrtGamma {
+    /// Creates a square root gamma strategy with default values:
+    /// - `gamma_factor`: 1.0
+    /// - `gamma_max`: 0.25
+    fn default() -> Self {
+        Self {
+            gamma_factor: 1.0,
+            gamma_max: 0.25,
+        }
+    }
+}
+
+impl GammaStrategy for SqrtGamma {
+    #[allow(clippy::cast_precision_loss)]
+    fn gamma(&self, n_trials: usize) -> f64 {
+        if n_trials == 0 {
+            return self.gamma_max;
+        }
+        let n_good = (self.gamma_factor / (n_trials as f64).sqrt()).max(1.0);
+        (n_good / n_trials as f64).min(self.gamma_max)
+    }
+
+    fn clone_box(&self) -> Box<dyn GammaStrategy> {
+        Box::new(*self)
+    }
+}
+
+/// A Hyperopt-style gamma strategy.
+///
+/// This strategy computes gamma as `min(gamma_max, (gamma_base + 1) / n_trials)`,
+/// which is inspired by the original Hyperopt TPE implementation.
+///
+/// # Formula
+///
+/// ```text
+/// gamma = min(gamma_max, (gamma_base + 1) / n_trials)
+/// ```
+///
+/// When `n_trials` is 0, returns `gamma_max`.
+///
+/// # Examples
+///
+/// ```
+/// use optimizer::sampler::tpe::{GammaStrategy, HyperoptGamma};
+///
+/// // With gamma_base=24 and gamma_max=0.5:
+/// // - At n=25: gamma = min(0.5, 25/25) = 0.5 (capped)
+/// // - At n=100: gamma = min(0.5, 25/100) = 0.25
+/// let strategy = HyperoptGamma::new(24.0, 0.5).unwrap();
+///
+/// // Early trials have higher gamma
+/// let g50 = strategy.gamma(50);
+/// let g200 = strategy.gamma(200);
+/// assert!(g50 > g200, "Gamma should decrease with more trials");
+/// ```
+#[derive(Debug, Clone, Copy)]
+pub struct HyperoptGamma {
+    gamma_base: f64,
+    gamma_max: f64,
+}
+
+impl HyperoptGamma {
+    /// Creates a new Hyperopt-style gamma strategy.
+    ///
+    /// # Arguments
+    ///
+    /// * `gamma_base` - The base value added to 1 in the numerator.
+    /// * `gamma_max` - The maximum gamma value.
+    ///
+    /// # Errors
+    ///
+    /// Returns `Error::InvalidGamma` if:
+    /// - `gamma_base` is negative
+    /// - `gamma_max` is not in (0.0, 1.0)
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use optimizer::sampler::tpe::HyperoptGamma;
+    ///
+    /// let strategy = HyperoptGamma::new(24.0, 0.25).unwrap();
+    /// ```
+    pub fn new(gamma_base: f64, gamma_max: f64) -> crate::Result<Self> {
+        if gamma_base < 0.0 {
+            return Err(Error::InvalidGamma(gamma_base));
+        }
+        if gamma_max <= 0.0 || gamma_max >= 1.0 {
+            return Err(Error::InvalidGamma(gamma_max));
+        }
+        Ok(Self {
+            gamma_base,
+            gamma_max,
+        })
+    }
+
+    /// Returns the gamma base value.
+    #[must_use]
+    pub fn gamma_base(&self) -> f64 {
+        self.gamma_base
+    }
+
+    /// Returns the maximum gamma value.
+    #[must_use]
+    pub fn gamma_max(&self) -> f64 {
+        self.gamma_max
+    }
+}
+
+impl Default for HyperoptGamma {
+    /// Creates a Hyperopt-style gamma strategy with default values:
+    /// - `gamma_base`: 24.0
+    /// - `gamma_max`: 0.25
+    fn default() -> Self {
+        Self {
+            gamma_base: 24.0,
+            gamma_max: 0.25,
+        }
+    }
+}
+
+impl GammaStrategy for HyperoptGamma {
+    #[allow(clippy::cast_precision_loss)]
+    fn gamma(&self, n_trials: usize) -> f64 {
+        if n_trials == 0 {
+            return self.gamma_max;
+        }
+        ((self.gamma_base + 1.0) / n_trials as f64).min(self.gamma_max)
+    }
+
+    fn clone_box(&self) -> Box<dyn GammaStrategy> {
+        Box::new(*self)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::sampler::tpe::TpeSampler;
+
+    #[test]
+    fn test_fixed_gamma_default() {
+        let strategy = FixedGamma::default();
+        assert!((strategy.gamma(0) - 0.25).abs() < f64::EPSILON);
+        assert!((strategy.gamma(100) - 0.25).abs() < f64::EPSILON);
+        assert!((strategy.value() - 0.25).abs() < f64::EPSILON);
+    }
+
+    #[test]
+    fn test_fixed_gamma_custom() {
+        let strategy = FixedGamma::new(0.15).unwrap();
+        assert!((strategy.gamma(0) - 0.15).abs() < f64::EPSILON);
+        assert!((strategy.gamma(50) - 0.15).abs() < f64::EPSILON);
+        assert!((strategy.gamma(1000) - 0.15).abs() < f64::EPSILON);
+    }
+
+    #[test]
+    fn test_fixed_gamma_invalid() {
+        assert!(FixedGamma::new(0.0).is_err());
+        assert!(FixedGamma::new(1.0).is_err());
+        assert!(FixedGamma::new(-0.1).is_err());
+        assert!(FixedGamma::new(1.5).is_err());
+    }
+
+    #[test]
+    fn test_linear_gamma_default() {
+        let strategy = LinearGamma::default();
+        assert!((strategy.gamma(0) - 0.10).abs() < f64::EPSILON);
+        assert!((strategy.gamma(50) - 0.175).abs() < f64::EPSILON); // midpoint
+        assert!((strategy.gamma(100) - 0.25).abs() < f64::EPSILON);
+        assert!((strategy.gamma(200) - 0.25).abs() < f64::EPSILON); // capped
+    }
+
+    #[test]
+    fn test_linear_gamma_custom() {
+        let strategy = LinearGamma::new(0.1, 0.4, 100).unwrap();
+        assert!((strategy.gamma(0) - 0.1).abs() < f64::EPSILON);
+        assert!((strategy.gamma(50) - 0.25).abs() < f64::EPSILON);
+        assert!((strategy.gamma(100) - 0.4).abs() < f64::EPSILON);
+        assert!((strategy.gamma(200) - 0.4).abs() < f64::EPSILON);
+    }
+
+    #[test]
+    fn test_linear_gamma_invalid() {
+        assert!(LinearGamma::new(0.0, 0.5, 100).is_err());
+        assert!(LinearGamma::new(0.1, 1.0, 100).is_err());
+        assert!(LinearGamma::new(0.5, 0.2, 100).is_err()); // min > max
+    }
+
+    #[test]
+    fn test_sqrt_gamma_default() {
+        let strategy = SqrtGamma::default();
+        // At n=0, returns gamma_max
+        assert!((strategy.gamma(0) - 0.25).abs() < f64::EPSILON);
+
+        // gamma decreases with more trials
+        let g10 = strategy.gamma(10);
+        let g100 = strategy.gamma(100);
+        assert!(g10 > g100);
+    }
+
+    #[test]
+    fn test_sqrt_gamma_custom() {
+        let strategy = SqrtGamma::new(2.0, 0.5).unwrap();
+        assert!((strategy.gamma(0) - 0.5).abs() < f64::EPSILON);
+
+        // At n=4: n_good = max(1, 2/2) = 1, gamma = 1/4 = 0.25
+        let g4 = strategy.gamma(4);
+        assert!((g4 - 0.25).abs() < f64::EPSILON);
+    }
+
+    #[test]
+    fn test_sqrt_gamma_invalid() {
+        assert!(SqrtGamma::new(0.0, 0.25).is_err()); // factor must be positive
+        assert!(SqrtGamma::new(-1.0, 0.25).is_err());
+        assert!(SqrtGamma::new(1.0, 0.0).is_err());
+        assert!(SqrtGamma::new(1.0, 1.0).is_err());
+    }
+
+    #[test]
+    fn test_hyperopt_gamma_default() {
+        let strategy = HyperoptGamma::default();
+        // At n=0, returns gamma_max
+        assert!((strategy.gamma(0) - 0.25).abs() < f64::EPSILON);
+
+        // At n=100: (24+1)/100 = 0.25, so capped to 0.25
+        assert!((strategy.gamma(100) - 0.25).abs() < f64::EPSILON);
+
+        // At n=200: (24+1)/200 = 0.125
+        assert!((strategy.gamma(200) - 0.125).abs() < f64::EPSILON);
+    }
+
+    #[test]
+    fn test_hyperopt_gamma_custom() {
+        let strategy = HyperoptGamma::new(9.0, 0.5).unwrap();
+        // At n=20: (9+1)/20 = 0.5, capped to 0.5
+        assert!((strategy.gamma(20) - 0.5).abs() < f64::EPSILON);
+
+        // At n=100: (9+1)/100 = 0.1
+        assert!((strategy.gamma(100) - 0.1).abs() < f64::EPSILON);
+    }
+
+    #[test]
+    fn test_hyperopt_gamma_invalid() {
+        assert!(HyperoptGamma::new(-1.0, 0.25).is_err());
+        assert!(HyperoptGamma::new(24.0, 0.0).is_err());
+        assert!(HyperoptGamma::new(24.0, 1.0).is_err());
+    }
+
+    #[test]
+    fn test_gamma_strategy_clone_box() {
+        let fixed: Box<dyn GammaStrategy> = Box::new(FixedGamma::new(0.3).unwrap());
+        let cloned = fixed.clone();
+        assert!((cloned.gamma(0) - 0.3).abs() < f64::EPSILON);
+
+        let linear: Box<dyn GammaStrategy> = Box::new(LinearGamma::default());
+        let cloned = linear.clone();
+        assert!((cloned.gamma(0) - 0.10).abs() < f64::EPSILON);
+    }
+
+    #[test]
+    fn test_tpe_with_linear_gamma_strategy() {
+        let sampler = TpeSampler::builder()
+            .gamma_strategy(LinearGamma::new(0.1, 0.3, 50).unwrap())
+            .n_startup_trials(5)
+            .seed(42)
+            .build()
+            .unwrap();
+
+        // Verify the strategy is applied
+        let g = sampler.gamma_strategy().gamma(25);
+        assert!((g - 0.2).abs() < f64::EPSILON); // midpoint of 0.1 to 0.3
+    }
+
+    #[test]
+    fn test_gamma_overrides_gamma_strategy() {
+        // When gamma() is called after gamma_strategy(), it should take precedence
+        let sampler = TpeSampler::builder()
+            .gamma_strategy(SqrtGamma::default())
+            .gamma(0.15) // This should override
+            .build()
+            .unwrap();
+
+        // Should use fixed gamma of 0.15
+        assert!((sampler.gamma_strategy().gamma(0) - 0.15).abs() < f64::EPSILON);
+        assert!((sampler.gamma_strategy().gamma(100) - 0.15).abs() < f64::EPSILON);
+    }
+
+    #[test]
+    fn test_gamma_strategy_overrides_gamma() {
+        // When gamma_strategy() is called after gamma(), it should take precedence
+        let sampler = TpeSampler::builder()
+            .gamma(0.15)
+            .gamma_strategy(SqrtGamma::default()) // This should override
+            .build()
+            .unwrap();
+
+        // Should use SqrtGamma - gamma decreases with trials
+        let g10 = sampler.gamma_strategy().gamma(10);
+        let g100 = sampler.gamma_strategy().gamma(100);
+        assert!(g10 > g100, "SqrtGamma should decrease with more trials");
+    }
+
+    #[test]
+    fn test_custom_gamma_strategy() {
+        #[derive(Debug, Clone)]
+        struct DoubleGamma;
+
+        impl GammaStrategy for DoubleGamma {
+            fn gamma(&self, n_trials: usize) -> f64 {
+                // Double the trial count-based calculation, capped at 0.5
+                #[allow(clippy::cast_precision_loss)]
+                (0.01 * n_trials as f64).min(0.5)
+            }
+
+            fn clone_box(&self) -> Box<dyn GammaStrategy> {
+                Box::new(self.clone())
+            }
+        }
+
+        let sampler = TpeSampler::builder()
+            .gamma_strategy(DoubleGamma)
+            .build()
+            .unwrap();
+
+        assert!((sampler.gamma_strategy().gamma(10) - 0.1).abs() < f64::EPSILON);
+        assert!((sampler.gamma_strategy().gamma(50) - 0.5).abs() < f64::EPSILON);
+        assert!((sampler.gamma_strategy().gamma(100) - 0.5).abs() < f64::EPSILON);
+    }
+}

src/sampler/tpe/mod.rs

@@ -0,0 +1,12 @@
+//! Tree-Parzen Estimator (TPE) sampler implementation and utilities.
+//!
+//! This module provides TPE-based sampling for Bayesian optimization,
+//! including support for intersection search space calculation.
+
+mod gamma;
+mod sampler;
+pub mod search_space;
+
+pub use gamma::{FixedGamma, GammaStrategy, HyperoptGamma, LinearGamma, SqrtGamma};
+pub use sampler::{TpeSampler, TpeSamplerBuilder};
+pub use search_space::{GroupDecomposedSearchSpace, IntersectionSearchSpace};

src/sampler/tpe/sampler.rs

@@ -3,17 +3,80 @@
 //! TPE is a Bayesian optimization algorithm that models the objective function
 //! using two probability distributions: one for promising (good) parameter values
 //! and one for unpromising (bad) parameter values.
+//!
+//! # Gamma Strategies
+//!
+//! The gamma parameter controls what fraction of trials are considered "good".
+//! This module provides several built-in strategies via the [`GammaStrategy`] trait:
+//!
+//! - [`FixedGamma`]: Constant gamma value (default: 0.25)
+//! - [`LinearGamma`]: Linear interpolation between min and max based on trial count
+//! - [`SqrtGamma`]: Gamma decreases as 1/√n (similar to Optuna)
+//! - [`HyperoptGamma`]: Hyperopt-style adaptive gamma
+//!
+//! You can also implement your own strategy by implementing the [`GammaStrategy`] trait.
+//!
+//! # Examples
+//!
+//! Using a built-in gamma strategy:
+//!
+//! ```
+//! use optimizer::sampler::tpe::{SqrtGamma, TpeSampler};
+//!
+//! let sampler = TpeSampler::builder()
+//!     .gamma_strategy(SqrtGamma::default())
+//!     .build()
+//!     .unwrap();
+//! ```
+//!
+//! Implementing a custom gamma strategy:
+//!
+//! ```
+//! use optimizer::sampler::tpe::{GammaStrategy, TpeSampler};
+//!
+//! #[derive(Debug, Clone)]
+//! struct MyGamma {
+//!     base: f64,
+//! }
+//!
+//! impl GammaStrategy for MyGamma {
+//!     fn gamma(&self, n_trials: usize) -> f64 {
+//!         (self.base + 0.01 * n_trials as f64).min(0.5)
+//!     }
+//!
+//!     fn clone_box(&self) -> Box<dyn GammaStrategy> {
+//!         Box::new(self.clone())
+//!     }
+//! }
+//!
+//! let sampler = TpeSampler::builder()
+//!     .gamma_strategy(MyGamma { base: 0.1 })
+//!     .build()
+//!     .unwrap();
+//! ```
+
+use core::fmt::Debug;
+use std::sync::Arc;
 
 use parking_lot::Mutex;
 use rand::rngs::StdRng;
 use rand::{Rng, SeedableRng};
 
 use crate::distribution::Distribution;
-use crate::error::{Result, TpeError};
+use crate::error::{Error, Result};
 use crate::kde::KernelDensityEstimator;
 use crate::param::ParamValue;
+use crate::sampler::tpe::gamma::{FixedGamma, GammaStrategy};
 use crate::sampler::{CompletedTrial, Sampler};
 
+// ============================================================================
+// Gamma Strategy Trait and Implementations
+// ============================================================================
+
+// ============================================================================
+// TPE Sampler
+// ============================================================================
+
 /// A Tree-Parzen Estimator (TPE) sampler for Bayesian optimization.
 ///
 /// TPE works by splitting completed trials into two groups based on their
@@ -25,26 +88,42 @@ use crate::sampler::{CompletedTrial, Sampler};
 /// During the startup phase (when fewer than `n_startup_trials` are completed),
 /// TPE falls back to random sampling to gather initial data.
 ///
+/// # Gamma Strategies
+///
+/// The gamma quantile can be configured using different strategies via the
+/// [`GammaStrategy`] trait.
+///
 /// # Examples
 ///
 /// ```
 /// use optimizer::sampler::tpe::TpeSampler;
 ///
-/// // Create with default settings
+/// // Create with default settings (FixedGamma at 0.25)
 /// let sampler = TpeSampler::new();
 ///
 /// // Create with custom settings using the builder
 /// let sampler = TpeSampler::builder()
-///     .gamma(0.15)
+///     .gamma(0.15)  // Shorthand for Fixednew(0.15)
 ///     .n_startup_trials(20)
 ///     .n_ei_candidates(32)
 ///     .seed(42)
 ///     .build()
 ///     .unwrap();
 /// ```
+///
+/// Using a different gamma strategy:
+///
+/// ```
+/// use optimizer::sampler::tpe::{SqrtGamma, TpeSampler};
+///
+/// let sampler = TpeSampler::builder()
+///     .gamma_strategy(SqrtGamma::default())
+///     .build()
+///     .unwrap();
+/// ```
 pub struct TpeSampler {
-    /// Fraction of trials to consider as "good" (gamma quantile).
-    gamma: f64,
+    /// Strategy for computing the gamma quantile.
+    gamma_strategy: Arc<dyn GammaStrategy>,
     /// Number of trials before TPE kicks in (uses random sampling before this).
     n_startup_trials: usize,
     /// Number of candidate samples to evaluate when selecting the next point.
@@ -59,14 +138,14 @@ impl TpeSampler {
     /// Creates a new TPE sampler with default settings.
     ///
     /// Default settings:
-    /// - gamma: 0.25 (top 25% of trials are considered "good")
+    /// - gamma strategy: [`FixedGamma`] with gamma = 0.25
     /// - `n_startup_trials`: 10 (random sampling for first 10 trials)
     /// - `n_ei_candidates`: 24 (evaluate 24 candidates per sample)
     /// - `kde_bandwidth`: None (uses Scott's rule for automatic bandwidth)
     #[must_use]
     pub fn new() -> Self {
         Self {
-            gamma: 0.25,
+            gamma_strategy: Arc::new(FixedGamma::default()),
             n_startup_trials: 10,
             n_ei_candidates: 24,
             kde_bandwidth: None,
@@ -96,6 +175,10 @@ impl TpeSampler {
 
     /// Creates a new TPE sampler with custom configuration.
     ///
+    /// This method uses a fixed gamma value. For more advanced gamma strategies,
+    /// use [`TpeSampler::with_strategy`] or the builder pattern with
+    /// [`TpeSamplerBuilder::gamma_strategy`].
+    ///
     /// # Arguments
     ///
     /// * `gamma` - Fraction of trials to consider "good" (0.0 to 1.0).
@@ -106,8 +189,8 @@ impl TpeSampler {
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::InvalidGamma` if gamma is not in (0.0, 1.0).
-    /// Returns `TpeError::InvalidBandwidth` if `kde_bandwidth` is Some but not positive.
+    /// Returns `Error::InvalidGamma` if gamma is not in (0.0, 1.0).
+    /// Returns `Error::InvalidBandwidth` if `kde_bandwidth` is Some but not positive.
     pub fn with_config(
         gamma: f64,
         n_startup_trials: usize,
@@ -115,13 +198,55 @@ impl TpeSampler {
         kde_bandwidth: Option<f64>,
         seed: Option<u64>,
     ) -> Result<Self> {
-        if gamma <= 0.0 || gamma >= 1.0 {
-            return Err(TpeError::InvalidGamma(gamma));
-        }
+        let gamma_strategy = FixedGamma::new(gamma)?;
+        Self::with_strategy(
+            gamma_strategy,
+            n_startup_trials,
+            n_ei_candidates,
+            kde_bandwidth,
+            seed,
+        )
+    }
+
+    /// Creates a new TPE sampler with a custom gamma strategy.
+    ///
+    /// # Arguments
+    ///
+    /// * `gamma_strategy` - The strategy for computing the gamma quantile.
+    /// * `n_startup_trials` - Number of random trials before TPE sampling.
+    /// * `n_ei_candidates` - Number of candidates to evaluate per sample.
+    /// * `kde_bandwidth` - Optional fixed bandwidth for KDE. If None, uses Scott's rule.
+    /// * `seed` - Optional seed for reproducibility.
+    ///
+    /// # Errors
+    ///
+    /// Returns `Error::InvalidBandwidth` if `kde_bandwidth` is Some but not positive.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use optimizer::sampler::tpe::{SqrtGamma, TpeSampler};
+    ///
+    /// let sampler = TpeSampler::with_strategy(
+    ///     SqrtGamma::default(),
+    ///     10,       // n_startup_trials
+    ///     24,       // n_ei_candidates
+    ///     None,     // kde_bandwidth
+    ///     Some(42), // seed
+    /// )
+    /// .unwrap();
+    /// ```
+    pub fn with_strategy<G: GammaStrategy + 'static>(
+        gamma_strategy: G,
+        n_startup_trials: usize,
+        n_ei_candidates: usize,
+        kde_bandwidth: Option<f64>,
+        seed: Option<u64>,
+    ) -> Result<Self> {
         if let Some(bw) = kde_bandwidth
             && bw <= 0.0
         {
-            return Err(TpeError::InvalidBandwidth(bw));
+            return Err(Error::InvalidBandwidth(bw));
         }
 
         let rng = match seed {
@@ -130,7 +255,7 @@ impl TpeSampler {
         };
 
         Ok(Self {
-            gamma,
+            gamma_strategy: Arc::new(gamma_strategy),
             n_startup_trials,
             n_ei_candidates,
             kde_bandwidth,
@@ -138,8 +263,16 @@ impl TpeSampler {
         })
     }
 
+    /// Returns the gamma strategy used by this sampler.
+    #[must_use]
+    pub fn gamma_strategy(&self) -> &dyn GammaStrategy {
+        self.gamma_strategy.as_ref()
+    }
+
     /// Splits trials into good and bad groups based on the gamma quantile.
     ///
+    /// The gamma value is computed dynamically using the configured [`GammaStrategy`].
+    ///
     /// Returns (`good_trials`, `bad_trials`) where `good_trials` contains trials
     /// with values below the gamma quantile (for minimization).
     #[allow(
@@ -164,9 +297,15 @@ impl TpeSampler {
                 .unwrap_or(core::cmp::Ordering::Equal)
         });
 
+        // Compute gamma using the strategy and clamp to valid range
+        let gamma = self
+            .gamma_strategy
+            .gamma(history.len())
+            .clamp(f64::EPSILON, 1.0 - f64::EPSILON);
+
         // Calculate the split point (gamma quantile)
         // Ensure at least 1 trial in each group if possible
-        let n_good = ((history.len() as f64 * self.gamma).ceil() as usize)
+        let n_good = ((history.len() as f64 * gamma).ceil() as usize)
             .max(1)
             .min(history.len() - 1);
 
@@ -421,6 +560,8 @@ impl Default for TpeSampler {
 ///
 /// # Examples
 ///
+/// Using a fixed gamma value:
+///
 /// ```
 /// use optimizer::sampler::tpe::TpeSamplerBuilder;
 ///
@@ -432,9 +573,23 @@ impl Default for TpeSampler {
 ///     .build()
 ///     .unwrap();
 /// ```
+///
+/// Using a custom gamma strategy:
+///
+/// ```
+/// use optimizer::sampler::tpe::{SqrtGamma, TpeSamplerBuilder};
+///
+/// let sampler = TpeSamplerBuilder::new()
+///     .gamma_strategy(SqrtGamma::default())
+///     .n_startup_trials(20)
+///     .build()
+///     .unwrap();
+/// ```
 #[derive(Debug, Clone)]
 pub struct TpeSamplerBuilder {
-    gamma: f64,
+    gamma_strategy: Box<dyn GammaStrategy>,
+    /// Raw gamma value for deferred validation (Some if `gamma()` was called)
+    raw_gamma: Option<f64>,
     n_startup_trials: usize,
     n_ei_candidates: usize,
     kde_bandwidth: Option<f64>,
@@ -445,7 +600,7 @@ impl TpeSamplerBuilder {
     /// Creates a new builder with default settings.
     ///
     /// Default settings:
-    /// - gamma: 0.25 (top 25% of trials are considered "good")
+    /// - gamma strategy: [`FixedGamma`] with gamma = 0.25
     /// - `n_startup_trials`: 10 (random sampling for first 10 trials)
     /// - `n_ei_candidates`: 24 (evaluate 24 candidates per sample)
     /// - `kde_bandwidth`: None (uses Scott's rule for automatic bandwidth)
@@ -453,7 +608,8 @@ impl TpeSamplerBuilder {
     #[must_use]
     pub fn new() -> Self {
         Self {
-            gamma: 0.25,
+            gamma_strategy: Box::new(FixedGamma::default()),
+            raw_gamma: None,
             n_startup_trials: 10,
             n_ei_candidates: 24,
             kde_bandwidth: None,
@@ -461,7 +617,10 @@ impl TpeSamplerBuilder {
         }
     }
 
-    /// Sets the gamma quantile for splitting trials into good/bad groups.
+    /// Sets a fixed gamma value for splitting trials into good/bad groups.
+    ///
+    /// This is a convenience method that creates a [`FixedGamma`] strategy.
+    /// For more advanced gamma strategies, use [`gamma_strategy`](Self::gamma_strategy).
     ///
     /// A gamma of 0.25 means the top 25% of trials (by objective value) are
     /// considered "good" and used to build the l(x) distribution.
@@ -484,10 +643,71 @@ impl TpeSamplerBuilder {
     /// # Note
     ///
     /// Validation happens at `build()` time. If gamma is not in (0.0, 1.0),
-    /// `build()` will return `Err(TpeError::InvalidGamma)`.
+    /// `build()` will return `Err(Error::InvalidGamma)`.
     #[must_use]
     pub fn gamma(mut self, gamma: f64) -> Self {
-        self.gamma = gamma;
+        // We defer validation to build() time for consistency with the existing API
+        // Store the raw value for validation later
+        self.raw_gamma = Some(gamma);
+        self
+    }
+
+    /// Sets a custom gamma strategy for splitting trials into good/bad groups.
+    ///
+    /// The gamma strategy determines what fraction of trials are considered
+    /// "good" based on the number of completed trials. This allows the gamma
+    /// value to adapt dynamically during optimization.
+    ///
+    /// # Arguments
+    ///
+    /// * `strategy` - A type implementing [`GammaStrategy`].
+    ///
+    /// # Examples
+    ///
+    /// Using built-in strategies:
+    ///
+    /// ```
+    /// use optimizer::sampler::tpe::{LinearGamma, SqrtGamma, TpeSamplerBuilder};
+    ///
+    /// // Square root strategy (Optuna-style)
+    /// let sampler = TpeSamplerBuilder::new()
+    ///     .gamma_strategy(SqrtGamma::default())
+    ///     .build()
+    ///     .unwrap();
+    ///
+    /// // Linear interpolation strategy
+    /// let sampler = TpeSamplerBuilder::new()
+    ///     .gamma_strategy(LinearGamma::new(0.1, 0.3, 50).unwrap())
+    ///     .build()
+    ///     .unwrap();
+    /// ```
+    ///
+    /// Using a custom strategy:
+    ///
+    /// ```
+    /// use optimizer::sampler::tpe::{GammaStrategy, TpeSamplerBuilder};
+    ///
+    /// #[derive(Debug, Clone)]
+    /// struct MyGamma;
+    ///
+    /// impl GammaStrategy for MyGamma {
+    ///     fn gamma(&self, n_trials: usize) -> f64 {
+    ///         0.25 // Always return 0.25
+    ///     }
+    ///     fn clone_box(&self) -> Box<dyn GammaStrategy> {
+    ///         Box::new(self.clone())
+    ///     }
+    /// }
+    ///
+    /// let sampler = TpeSamplerBuilder::new()
+    ///     .gamma_strategy(MyGamma)
+    ///     .build()
+    ///     .unwrap();
+    /// ```
+    #[must_use]
+    pub fn gamma_strategy<G: GammaStrategy + 'static>(mut self, strategy: G) -> Self {
+        self.gamma_strategy = Box::new(strategy);
+        self.raw_gamma = None; // Clear any raw gamma set by gamma()
         self
     }
 
@@ -569,7 +789,7 @@ impl TpeSamplerBuilder {
     /// # Note
     ///
     /// Validation happens at `build()` time. If bandwidth is not positive,
-    /// `build()` will return `Err(TpeError::InvalidBandwidth)`.
+    /// `build()` will return `Err(Error::InvalidBandwidth)`.
     #[must_use]
     pub fn kde_bandwidth(mut self, bandwidth: f64) -> Self {
         self.kde_bandwidth = Some(bandwidth);
@@ -602,8 +822,8 @@ impl TpeSamplerBuilder {
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::InvalidGamma` if gamma is not in (0.0, 1.0).
-    /// Returns `TpeError::InvalidBandwidth` if `kde_bandwidth` is Some but not positive.
+    /// Returns `Error::InvalidGamma` if a fixed gamma value was set and is not in (0.0, 1.0).
+    /// Returns `Error::InvalidBandwidth` if `kde_bandwidth` is Some but not positive.
     ///
     /// # Examples
     ///
@@ -619,13 +839,33 @@ impl TpeSamplerBuilder {
     ///     .unwrap();
     /// ```
     pub fn build(self) -> Result<TpeSampler> {
-        TpeSampler::with_config(
-            self.gamma,
-            self.n_startup_trials,
-            self.n_ei_candidates,
-            self.kde_bandwidth,
-            self.seed,
-        )
+        // Determine the gamma strategy to use
+        let gamma_strategy: Arc<dyn GammaStrategy> = if let Some(raw) = self.raw_gamma {
+            // Validate and create FixedGamma from raw value
+            Arc::new(FixedGamma::new(raw)?)
+        } else {
+            Arc::from(self.gamma_strategy)
+        };
+
+        // Validate bandwidth
+        if let Some(bw) = self.kde_bandwidth
+            && bw <= 0.0
+        {
+            return Err(Error::InvalidBandwidth(bw));
+        }
+
+        let rng = match self.seed {
+            Some(s) => StdRng::seed_from_u64(s),
+            None => StdRng::from_os_rng(),
+        };
+
+        Ok(TpeSampler {
+            gamma_strategy,
+            n_startup_trials: self.n_startup_trials,
+            n_ei_candidates: self.n_ei_candidates,
+            kde_bandwidth: self.kde_bandwidth,
+            rng: Mutex::new(rng),
+        })
     }
 }
 
@@ -801,7 +1041,8 @@ mod tests {
     #[test]
     fn test_tpe_sampler_new() {
         let sampler = TpeSampler::new();
-        assert!((sampler.gamma - 0.25).abs() < f64::EPSILON);
+        // Default uses FixedGamma with 0.25
+        assert!((sampler.gamma_strategy().gamma(0) - 0.25).abs() < f64::EPSILON);
         assert_eq!(sampler.n_startup_trials, 10);
         assert_eq!(sampler.n_ei_candidates, 24);
     }
@@ -809,7 +1050,8 @@ mod tests {
     #[test]
     fn test_tpe_sampler_with_config() {
         let sampler = TpeSampler::with_config(0.15, 20, 32, None, Some(42)).unwrap();
-        assert!((sampler.gamma - 0.15).abs() < f64::EPSILON);
+        // with_config uses FixedGamma
+        assert!((sampler.gamma_strategy().gamma(0) - 0.15).abs() < f64::EPSILON);
         assert_eq!(sampler.n_startup_trials, 20);
         assert_eq!(sampler.n_ei_candidates, 32);
     }
@@ -817,13 +1059,13 @@ mod tests {
     #[test]
     fn test_tpe_sampler_invalid_gamma_zero() {
         let result = TpeSampler::with_config(0.0, 10, 24, None, None);
-        assert!(matches!(result, Err(TpeError::InvalidGamma(_))));
+        assert!(matches!(result, Err(Error::InvalidGamma(_))));
     }
 
     #[test]
     fn test_tpe_sampler_invalid_gamma_one() {
         let result = TpeSampler::with_config(1.0, 10, 24, None, None);
-        assert!(matches!(result, Err(TpeError::InvalidGamma(_))));
+        assert!(matches!(result, Err(Error::InvalidGamma(_))));
     }
 
     #[test]
@@ -1033,7 +1275,7 @@ mod tests {
     fn test_tpe_sampler_builder_default() {
         let builder = TpeSamplerBuilder::new();
         let sampler = builder.build().unwrap();
-        assert!((sampler.gamma - 0.25).abs() < f64::EPSILON);
+        assert!((sampler.gamma_strategy().gamma(0) - 0.25).abs() < f64::EPSILON);
         assert_eq!(sampler.n_startup_trials, 10);
         assert_eq!(sampler.n_ei_candidates, 24);
     }
@@ -1047,7 +1289,7 @@ mod tests {
             .seed(42)
             .build()
             .unwrap();
-        assert!((sampler.gamma - 0.15).abs() < f64::EPSILON);
+        assert!((sampler.gamma_strategy().gamma(0) - 0.15).abs() < f64::EPSILON);
         assert_eq!(sampler.n_startup_trials, 20);
         assert_eq!(sampler.n_ei_candidates, 32);
     }
@@ -1060,7 +1302,7 @@ mod tests {
             .n_ei_candidates(48)
             .build()
             .unwrap();
-        assert!((sampler.gamma - 0.10).abs() < f64::EPSILON);
+        assert!((sampler.gamma_strategy().gamma(0) - 0.10).abs() < f64::EPSILON);
         assert_eq!(sampler.n_startup_trials, 15);
         assert_eq!(sampler.n_ei_candidates, 48);
     }
@@ -1069,7 +1311,7 @@ mod tests {
     fn test_tpe_sampler_builder_partial() {
         // Test setting only some options
         let sampler = TpeSamplerBuilder::new().gamma(0.20).build().unwrap();
-        assert!((sampler.gamma - 0.20).abs() < f64::EPSILON);
+        assert!((sampler.gamma_strategy().gamma(0) - 0.20).abs() < f64::EPSILON);
         assert_eq!(sampler.n_startup_trials, 10); // default
         assert_eq!(sampler.n_ei_candidates, 24); // default
     }
@@ -1077,7 +1319,7 @@ mod tests {
     #[test]
     fn test_tpe_sampler_builder_invalid_gamma() {
         let result = TpeSamplerBuilder::new().gamma(1.5).build();
-        assert!(matches!(result, Err(TpeError::InvalidGamma(_))));
+        assert!(matches!(result, Err(Error::InvalidGamma(_))));
     }
 
     #[test]

src/study.rs

@@ -275,7 +275,7 @@ where
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::NoCompletedTrials` if no trials have been completed.
+    /// Returns `Error::NoCompletedTrials` if no trials have been completed.
     ///
     /// # Examples
     ///
@@ -305,7 +305,7 @@ where
         let trials = self.completed_trials.read();
 
         if trials.is_empty() {
-            return Err(crate::TpeError::NoCompletedTrials);
+            return Err(crate::Error::NoCompletedTrials);
         }
 
         let best = trials
@@ -325,7 +325,7 @@ where
                     }
                 }
             })
-            .ok_or(crate::TpeError::NoCompletedTrials)?;
+            .ok_or(crate::Error::NoCompletedTrials)?;
 
         Ok(best.clone())
     }
@@ -338,7 +338,7 @@ where
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::NoCompletedTrials` if no trials have been completed.
+    /// Returns `Error::NoCompletedTrials` if no trials have been completed.
     ///
     /// # Examples
     ///
@@ -387,7 +387,7 @@ where
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::NoCompletedTrials` if all trials failed (no successful trials).
+    /// Returns `Error::NoCompletedTrials` if all trials failed (no successful trials).
     ///
     /// # Examples
     ///
@@ -402,7 +402,7 @@ where
     /// study
     ///     .optimize(10, |trial| {
     ///         let x = trial.suggest_float("x", -10.0, 10.0)?;
-    ///         Ok::<_, optimizer::TpeError>(x * x)
+    ///         Ok::<_, optimizer::Error>(x * x)
     ///     })
     ///     .unwrap();
     ///
@@ -431,7 +431,7 @@ where
 
         // Return error if no trials succeeded
         if self.n_trials() == 0 {
-            return Err(crate::TpeError::NoCompletedTrials);
+            return Err(crate::Error::NoCompletedTrials);
         }
 
         Ok(())
@@ -455,7 +455,7 @@ where
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::NoCompletedTrials` if all trials failed (no successful trials).
+    /// Returns `Error::NoCompletedTrials` if all trials failed (no successful trials).
     ///
     /// # Examples
     ///
@@ -474,7 +474,7 @@ where
     ///         let x = trial.suggest_float("x", -10.0, 10.0)?;
     ///         // Simulate async work (e.g., network request)
     ///         let value = x * x;
-    ///         Ok::<_, optimizer::TpeError>((trial, value))
+    ///         Ok::<_, optimizer::Error>((trial, value))
     ///     })
     ///     .await?;
     ///
@@ -511,7 +511,7 @@ where
 
         // Return error if no trials succeeded
         if self.n_trials() == 0 {
-            return Err(crate::TpeError::NoCompletedTrials);
+            return Err(crate::Error::NoCompletedTrials);
         }
 
         Ok(())
@@ -536,8 +536,8 @@ where
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::NoCompletedTrials` if all trials failed (no successful trials).
-    /// Returns `TpeError::TaskError` if the semaphore is closed or a spawned task panics.
+    /// Returns `Error::NoCompletedTrials` if all trials failed (no successful trials).
+    /// Returns `Error::TaskError` if the semaphore is closed or a spawned task panics.
     ///
     /// # Examples
     ///
@@ -556,7 +556,7 @@ where
     ///         let x = trial.suggest_float("x", -10.0, 10.0)?;
     ///         // Async objective function (e.g., network request)
     ///         let value = x * x;
-    ///         Ok::<_, optimizer::TpeError>((trial, value))
+    ///         Ok::<_, optimizer::Error>((trial, value))
     ///     })
     ///     .await?;
     ///
@@ -590,7 +590,7 @@ where
                 .clone()
                 .acquire_owned()
                 .await
-                .map_err(|e| crate::TpeError::TaskError(e.to_string()))?;
+                .map_err(|e| crate::Error::TaskError(e.to_string()))?;
             let trial = self.create_trial();
             let objective = Arc::clone(&objective);
 
@@ -607,7 +607,7 @@ where
         for handle in handles {
             match handle
                 .await
-                .map_err(|e| crate::TpeError::TaskError(e.to_string()))?
+                .map_err(|e| crate::Error::TaskError(e.to_string()))?
             {
                 Ok((trial, value)) => {
                     self.complete_trial(trial, value);
@@ -620,7 +620,7 @@ where
 
         // Return error if no trials succeeded
         if self.n_trials() == 0 {
-            return Err(crate::TpeError::NoCompletedTrials);
+            return Err(crate::Error::NoCompletedTrials);
         }
 
         Ok(())
@@ -643,9 +643,9 @@ where
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::NoCompletedTrials` if no trials completed successfully
+    /// Returns `Error::NoCompletedTrials` if no trials completed successfully
     /// before optimization stopped (either by completing all trials or early stopping).
-    /// Returns `TpeError::Internal` if a completed trial is not found after adding (internal invariant violation).
+    /// Returns `Error::Internal` if a completed trial is not found after adding (internal invariant violation).
     ///
     /// # Examples
     ///
@@ -664,7 +664,7 @@ where
     ///         100,
     ///         |trial| {
     ///             let x = trial.suggest_float("x", -10.0, 10.0)?;
-    ///             Ok::<_, optimizer::TpeError>(x * x)
+    ///             Ok::<_, optimizer::Error>(x * x)
     ///         },
     ///         |_study, completed_trial| {
     ///             // Stop early if we find a value less than 1.0
@@ -702,7 +702,7 @@ where
                     // Get the just-completed trial for the callback
                     let trials = self.completed_trials.read();
                     let Some(completed) = trials.last() else {
-                        return Err(crate::TpeError::Internal(
+                        return Err(crate::Error::Internal(
                             "completed trial not found after adding",
                         ));
                     };
@@ -725,7 +725,7 @@ where
 
         // Return error if no trials succeeded
         if self.n_trials() == 0 {
-            return Err(crate::TpeError::NoCompletedTrials);
+            return Err(crate::Error::NoCompletedTrials);
         }
 
         Ok(())
@@ -783,7 +783,7 @@ impl Study<f64> {
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::NoCompletedTrials` if all trials failed (no successful trials).
+    /// Returns `Error::NoCompletedTrials` if all trials failed (no successful trials).
     ///
     /// # Examples
     ///
@@ -798,7 +798,7 @@ impl Study<f64> {
     /// study
     ///     .optimize_with_sampler(10, |trial| {
     ///         let x = trial.suggest_float("x", -10.0, 10.0)?;
-    ///         Ok::<_, optimizer::TpeError>(x * x)
+    ///         Ok::<_, optimizer::Error>(x * x)
     ///     })
     ///     .unwrap();
     ///
@@ -829,7 +829,7 @@ impl Study<f64> {
 
         // Return error if no trials succeeded
         if self.n_trials() == 0 {
-            return Err(crate::TpeError::NoCompletedTrials);
+            return Err(crate::Error::NoCompletedTrials);
         }
 
         Ok(())
@@ -851,8 +851,8 @@ impl Study<f64> {
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::NoCompletedTrials` if no trials completed successfully.
-    /// Returns `TpeError::Internal` if a completed trial is not found after adding (internal invariant violation).
+    /// Returns `Error::NoCompletedTrials` if no trials completed successfully.
+    /// Returns `Error::Internal` if a completed trial is not found after adding (internal invariant violation).
     ///
     /// # Examples
     ///
@@ -871,7 +871,7 @@ impl Study<f64> {
     ///         100,
     ///         |trial| {
     ///             let x = trial.suggest_float("x", -10.0, 10.0)?;
-    ///             Ok::<_, optimizer::TpeError>(x * x)
+    ///             Ok::<_, optimizer::Error>(x * x)
     ///         },
     ///         |study, _completed_trial| {
     ///             // Stop after finding 5 good trials
@@ -907,7 +907,7 @@ impl Study<f64> {
                     // Get the just-completed trial for the callback
                     let trials = self.completed_trials.read();
                     let Some(completed) = trials.last() else {
-                        return Err(crate::TpeError::Internal(
+                        return Err(crate::Error::Internal(
                             "completed trial not found after adding",
                         ));
                     };
@@ -930,7 +930,7 @@ impl Study<f64> {
 
         // Return error if no trials succeeded
         if self.n_trials() == 0 {
-            return Err(crate::TpeError::NoCompletedTrials);
+            return Err(crate::Error::NoCompletedTrials);
         }
 
         Ok(())
@@ -953,7 +953,7 @@ impl Study<f64> {
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::NoCompletedTrials` if all trials failed (no successful trials).
+    /// Returns `Error::NoCompletedTrials` if all trials failed (no successful trials).
     ///
     /// # Examples
     ///
@@ -972,7 +972,7 @@ impl Study<f64> {
     ///         let x = trial.suggest_float("x", -10.0, 10.0)?;
     ///         // Simulate async work (e.g., network request)
     ///         let value = x * x;
-    ///         Ok::<_, optimizer::TpeError>((trial, value))
+    ///         Ok::<_, optimizer::Error>((trial, value))
     ///     })
     ///     .await?;
     ///
@@ -1009,7 +1009,7 @@ impl Study<f64> {
 
         // Return error if no trials succeeded
         if self.n_trials() == 0 {
-            return Err(crate::TpeError::NoCompletedTrials);
+            return Err(crate::Error::NoCompletedTrials);
         }
 
         Ok(())
@@ -1034,8 +1034,8 @@ impl Study<f64> {
     ///
     /// # Errors
     ///
-    /// Returns `TpeError::NoCompletedTrials` if all trials failed (no successful trials).
-    /// Returns `TpeError::TaskError` if the semaphore is closed or a spawned task panics.
+    /// Returns `Error::NoCompletedTrials` if all trials failed (no successful trials).
+    /// Returns `Error::TaskError` if the semaphore is closed or a spawned task panics.
     ///
     /// # Examples
     ///
@@ -1054,7 +1054,7 @@ impl Study<f64> {
     ///         let x = trial.suggest_float("x", -10.0, 10.0)?;
     ///         // Async objective function (e.g., network request)
     ///         let value = x * x;
-    ///         Ok::<_, optimizer::TpeError>((trial, value))
+    ///         Ok::<_, optimizer::Error>((trial, value))
     ///     })
     ///     .await?;
     ///
@@ -1087,7 +1087,7 @@ impl Study<f64> {
                 .clone()
                 .acquire_owned()
                 .await
-                .map_err(|e| crate::TpeError::TaskError(e.to_string()))?;
+                .map_err(|e| crate::Error::TaskError(e.to_string()))?;
             let trial = self.create_trial_with_sampler();
             let objective = Arc::clone(&objective);
 
@@ -1104,7 +1104,7 @@ impl Study<f64> {
         for handle in handles {
             match handle
                 .await
-                .map_err(|e| crate::TpeError::TaskError(e.to_string()))?
+                .map_err(|e| crate::Error::TaskError(e.to_string()))?
             {
                 Ok((trial, value)) => {
                     self.complete_trial(trial, value);
@@ -1117,7 +1117,7 @@ impl Study<f64> {
 
         // Return error if no trials succeeded
         if self.n_trials() == 0 {
-            return Err(crate::TpeError::NoCompletedTrials);
+            return Err(crate::Error::NoCompletedTrials);
         }
 
         Ok(())

src/trial.rs

@@ -1,5 +1,6 @@
 //! Trial implementation for tracking sampled parameters and trial state.
 
+use core::ops::{Range, RangeInclusive};
 use std::collections::HashMap;
 use std::sync::Arc;
 
@@ -8,11 +9,73 @@ use parking_lot::RwLock;
 use crate::distribution::{
     CategoricalDistribution, Distribution, FloatDistribution, IntDistribution,
 };
-use crate::error::{Result, TpeError};
+use crate::error::{Error, Result};
 use crate::param::ParamValue;
 use crate::sampler::{CompletedTrial, Sampler};
 use crate::types::TrialState;
 
+/// A trait for types that can be used with [`Trial::suggest_range`].
+///
+/// This trait is implemented for [`Range`] and [`RangeInclusive`] over `f64` and `i64`.
+/// It allows using Rust's range syntax directly with the optimizer.
+///
+/// # Supported Range Types
+///
+/// | Range Type | Example | Description |
+/// |------------|---------|-------------|
+/// | `Range<f64>` | `0.0..1.0` | Float range (end-exclusive, treated as inclusive for continuous sampling) |
+/// | `RangeInclusive<f64>` | `0.0..=1.0` | Float range (end-inclusive) |
+/// | `Range<i64>` | `1..10` | Integer range from 1 to 9 (end-exclusive) |
+/// | `RangeInclusive<i64>` | `1..=10` | Integer range from 1 to 10 (end-inclusive) |
+pub trait SuggestableRange {
+    /// The output type when suggesting from this range.
+    type Output;
+
+    /// Suggests a value from this range using the given trial.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the range is invalid (e.g., empty or low > high).
+    fn suggest(self, trial: &mut Trial, name: String) -> Result<Self::Output>;
+}
+
+impl SuggestableRange for Range<f64> {
+    type Output = f64;
+
+    fn suggest(self, trial: &mut Trial, name: String) -> Result<f64> {
+        trial.suggest_float(name, self.start, self.end)
+    }
+}
+
+impl SuggestableRange for RangeInclusive<f64> {
+    type Output = f64;
+
+    fn suggest(self, trial: &mut Trial, name: String) -> Result<f64> {
+        trial.suggest_float(name, *self.start(), *self.end())
+    }
+}
+
+impl SuggestableRange for Range<i64> {
+    type Output = i64;
+
+    fn suggest(self, trial: &mut Trial, name: String) -> Result<i64> {
+        // Range is exclusive on the end, so subtract 1
+        trial.suggest_int(
+            name,
+            self.start,
+            self.end.checked_sub(1).unwrap_or(self.end),
+        )
+    }
+}
+
+impl SuggestableRange for RangeInclusive<i64> {
+    type Output = i64;
+
+    fn suggest(self, trial: &mut Trial, name: String) -> Result<i64> {
+        trial.suggest_int(name, *self.start(), *self.end())
+    }
+}
+
 /// A trial represents a single evaluation of the objective function.
 ///
 /// Each trial has a unique ID and stores the sampled parameters along with
@@ -190,7 +253,7 @@ impl Trial {
     /// ```
     pub fn suggest_float(&mut self, name: impl Into<String>, low: f64, high: f64) -> Result<f64> {
         if low > high {
-            return Err(TpeError::InvalidBounds { low, high });
+            return Err(Error::InvalidBounds { low, high });
         }
 
         let name = name.into();
@@ -216,7 +279,7 @@ impl Trial {
                 }
             }
             // Distribution exists but doesn't match
-            return Err(TpeError::ParameterConflict {
+            return Err(Error::ParameterConflict {
                 name,
                 reason: "parameter was previously sampled with different bounds or type"
                     .to_string(),
@@ -226,7 +289,7 @@ impl Trial {
         // Sample using the sampler
         let dist = Distribution::Float(distribution);
         let ParamValue::Float(value) = self.sample_value(&dist) else {
-            return Err(TpeError::Internal(
+            return Err(Error::Internal(
                 "Float distribution should return Float value",
             ));
         };
@@ -283,11 +346,11 @@ impl Trial {
         high: f64,
     ) -> Result<f64> {
         if low <= 0.0 {
-            return Err(TpeError::InvalidLogBounds);
+            return Err(Error::InvalidLogBounds);
         }
 
         if low > high {
-            return Err(TpeError::InvalidBounds { low, high });
+            return Err(Error::InvalidBounds { low, high });
         }
 
         let name = name.into();
@@ -313,7 +376,7 @@ impl Trial {
                 }
             }
             // Distribution exists but doesn't match
-            return Err(TpeError::ParameterConflict {
+            return Err(Error::ParameterConflict {
                 name,
                 reason: "parameter was previously sampled with different bounds or type"
                     .to_string(),
@@ -323,7 +386,7 @@ impl Trial {
         // Sample using the sampler (sampler handles log-scale transformation)
         let dist = Distribution::Float(distribution);
         let ParamValue::Float(value) = self.sample_value(&dist) else {
-            return Err(TpeError::Internal(
+            return Err(Error::Internal(
                 "Float distribution should return Float value",
             ));
         };
@@ -380,11 +443,11 @@ impl Trial {
         step: f64,
     ) -> Result<f64> {
         if step <= 0.0 {
-            return Err(TpeError::InvalidStep);
+            return Err(Error::InvalidStep);
         }
 
         if low > high {
-            return Err(TpeError::InvalidBounds { low, high });
+            return Err(Error::InvalidBounds { low, high });
         }
 
         let name = name.into();
@@ -410,7 +473,7 @@ impl Trial {
                 }
             }
             // Distribution exists but doesn't match
-            return Err(TpeError::ParameterConflict {
+            return Err(Error::ParameterConflict {
                 name,
                 reason: "parameter was previously sampled with different bounds or type"
                     .to_string(),
@@ -420,7 +483,7 @@ impl Trial {
         // Sample using the sampler (sampler handles step-grid)
         let dist = Distribution::Float(distribution);
         let ParamValue::Float(value) = self.sample_value(&dist) else {
-            return Err(TpeError::Internal(
+            return Err(Error::Internal(
                 "Float distribution should return Float value",
             ));
         };
@@ -466,7 +529,7 @@ impl Trial {
     #[allow(clippy::cast_precision_loss)]
     pub fn suggest_int(&mut self, name: impl Into<String>, low: i64, high: i64) -> Result<i64> {
         if low > high {
-            return Err(TpeError::InvalidBounds {
+            return Err(Error::InvalidBounds {
                 low: low as f64,
                 high: high as f64,
             });
@@ -495,7 +558,7 @@ impl Trial {
                 }
             }
             // Distribution exists but doesn't match
-            return Err(TpeError::ParameterConflict {
+            return Err(Error::ParameterConflict {
                 name,
                 reason: "parameter was previously sampled with different bounds or type"
                     .to_string(),
@@ -505,9 +568,7 @@ impl Trial {
         // Sample using the sampler
         let dist = Distribution::Int(distribution);
         let ParamValue::Int(value) = self.sample_value(&dist) else {
-            return Err(TpeError::Internal(
-                "Int distribution should return Int value",
-            ));
+            return Err(Error::Internal("Int distribution should return Int value"));
         };
 
         // Store distribution and value
@@ -554,11 +615,11 @@ impl Trial {
     #[allow(clippy::cast_precision_loss)]
     pub fn suggest_int_log(&mut self, name: impl Into<String>, low: i64, high: i64) -> Result<i64> {
         if low < 1 {
-            return Err(TpeError::InvalidLogBounds);
+            return Err(Error::InvalidLogBounds);
         }
 
         if low > high {
-            return Err(TpeError::InvalidBounds {
+            return Err(Error::InvalidBounds {
                 low: low as f64,
                 high: high as f64,
             });
@@ -587,7 +648,7 @@ impl Trial {
                 }
             }
             // Distribution exists but doesn't match
-            return Err(TpeError::ParameterConflict {
+            return Err(Error::ParameterConflict {
                 name,
                 reason: "parameter was previously sampled with different bounds or type"
                     .to_string(),
@@ -597,9 +658,7 @@ impl Trial {
         // Sample using the sampler (sampler handles log-scale transformation)
         let dist = Distribution::Int(distribution);
         let ParamValue::Int(value) = self.sample_value(&dist) else {
-            return Err(TpeError::Internal(
-                "Int distribution should return Int value",
-            ));
+            return Err(Error::Internal("Int distribution should return Int value"));
         };
 
         // Store distribution and value
@@ -659,11 +718,11 @@ impl Trial {
         step: i64,
     ) -> Result<i64> {
         if step <= 0 {
-            return Err(TpeError::InvalidStep);
+            return Err(Error::InvalidStep);
         }
 
         if low > high {
-            return Err(TpeError::InvalidBounds {
+            return Err(Error::InvalidBounds {
                 low: low as f64,
                 high: high as f64,
             });
@@ -692,7 +751,7 @@ impl Trial {
                 }
             }
             // Distribution exists but doesn't match
-            return Err(TpeError::ParameterConflict {
+            return Err(Error::ParameterConflict {
                 name,
                 reason: "parameter was previously sampled with different bounds or type"
                     .to_string(),
@@ -702,9 +761,7 @@ impl Trial {
         // Sample using the sampler (sampler handles step-grid)
         let dist = Distribution::Int(distribution);
         let ParamValue::Int(value) = self.sample_value(&dist) else {
-            return Err(TpeError::Internal(
-                "Int distribution should return Int value",
-            ));
+            return Err(Error::Internal("Int distribution should return Int value"));
         };
 
         // Store distribution and value
@@ -760,7 +817,7 @@ impl Trial {
         choices: &[T],
     ) -> Result<T> {
         if choices.is_empty() {
-            return Err(TpeError::EmptyChoices);
+            return Err(Error::EmptyChoices);
         }
 
         let name = name.into();
@@ -779,7 +836,7 @@ impl Trial {
                 }
             }
             // Distribution exists but doesn't match
-            return Err(TpeError::ParameterConflict {
+            return Err(Error::ParameterConflict {
                 name,
                 reason: "parameter was previously sampled with different number of choices or type"
                     .to_string(),
@@ -789,7 +846,7 @@ impl Trial {
         // Sample using the sampler
         let dist = Distribution::Categorical(distribution);
         let ParamValue::Categorical(index) = self.sample_value(&dist) else {
-            return Err(TpeError::Internal(
+            return Err(Error::Internal(
                 "Categorical distribution should return Categorical value",
             ));
         };
@@ -800,4 +857,95 @@ impl Trial {
 
         Ok(choices[index].clone())
     }
+
+    /// Suggests a boolean parameter.
+    ///
+    /// The value is selected uniformly at random from `{false, true}`.
+    /// This is equivalent to calling `suggest_categorical(name, &[false, true])`.
+    ///
+    /// If the parameter has already been sampled, the cached value is returned.
+    /// If the parameter was sampled with a different type, a `ParameterConflict` error is returned.
+    ///
+    /// # Arguments
+    ///
+    /// * `name` - The name of the parameter.
+    ///
+    /// # Errors
+    ///
+    /// Returns `ParameterConflict` if the parameter was previously sampled with a different type.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use optimizer::Trial;
+    ///
+    /// let mut trial = Trial::new(0);
+    /// let use_dropout = trial.suggest_bool("use_dropout").unwrap();
+    /// assert!(use_dropout == true || use_dropout == false);
+    ///
+    /// // Calling again returns cached value
+    /// let use_dropout2 = trial.suggest_bool("use_dropout").unwrap();
+    /// assert_eq!(use_dropout, use_dropout2);
+    /// ```
+    pub fn suggest_bool(&mut self, name: impl Into<String>) -> Result<bool> {
+        self.suggest_categorical(name, &[false, true])
+    }
+
+    /// Suggests a parameter value from a range.
+    ///
+    /// This method accepts both [`Range`] (`..`) and [`RangeInclusive`] (`..=`)
+    /// for both `f64` and `i64` types, allowing natural Rust range syntax.
+    ///
+    /// For integer ranges, note that `Range` (`..`) is end-exclusive while
+    /// `RangeInclusive` (`..=`) is end-inclusive, matching Rust's semantics.
+    ///
+    /// If the parameter has already been sampled with the same bounds, the cached value is returned.
+    /// If the parameter was sampled with different bounds, a `ParameterConflict` error is returned.
+    ///
+    /// # Arguments
+    ///
+    /// * `name` - The name of the parameter.
+    /// * `range` - The range to sample from.
+    ///
+    /// # Type Parameters
+    ///
+    /// * `R` - A range type implementing [`SuggestableRange`].
+    ///
+    /// # Errors
+    ///
+    /// Returns `InvalidBounds` if the range is invalid (e.g., low > high or empty integer range).
+    /// Returns `ParameterConflict` if the parameter was previously sampled with different bounds.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use optimizer::Trial;
+    ///
+    /// let mut trial = Trial::new(0);
+    ///
+    /// // Float ranges
+    /// let x = trial.suggest_range("x", 0.0..1.0).unwrap();
+    /// assert!(x >= 0.0 && x <= 1.0);
+    ///
+    /// let y = trial.suggest_range("y", 0.0..=1.0).unwrap();
+    /// assert!(y >= 0.0 && y <= 1.0);
+    ///
+    /// // Integer ranges
+    /// let n = trial.suggest_range("n", 1_i64..10).unwrap(); // 1 to 9 inclusive
+    /// assert!(n >= 1 && n <= 9);
+    ///
+    /// let m = trial.suggest_range("m", 1_i64..=10).unwrap(); // 1 to 10 inclusive
+    /// assert!(m >= 1 && m <= 10);
+    ///
+    /// // Calling again with same range returns cached value
+    /// let x2 = trial.suggest_range("x", 0.0..1.0).unwrap();
+    /// assert_eq!(x, x2);
+    /// ```
+    pub fn suggest_range<R: SuggestableRange>(
+        &mut self,
+        name: impl Into<String>,
+        range: R,
+    ) -> Result<R::Output> {
+        range.suggest(self, name.into())
+    }
 }

tests/async_tests.rs

@@ -6,7 +6,7 @@
 
 use optimizer::sampler::random::RandomSampler;
 use optimizer::sampler::tpe::TpeSampler;
-use optimizer::{Direction, Study, TpeError};
+use optimizer::{Direction, Error, Study};
 
 #[tokio::test]
 async fn test_optimize_async_basic() {
@@ -16,7 +16,7 @@ async fn test_optimize_async_basic() {
     study
         .optimize_async(10, |mut trial| async move {
             let x = trial.suggest_float("x", -10.0, 10.0)?;
-            Ok::<_, TpeError>((trial, x * x))
+            Ok::<_, Error>((trial, x * x))
         })
         .await
         .expect("async optimization should succeed");
@@ -39,7 +39,7 @@ async fn test_optimize_async_with_sampler() {
     study
         .optimize_async_with_sampler(15, |mut trial| async move {
             let x = trial.suggest_float("x", -5.0, 5.0)?;
-            Ok::<_, TpeError>((trial, x * x))
+            Ok::<_, Error>((trial, x * x))
         })
         .await
         .expect("async optimization with sampler should succeed");
@@ -57,7 +57,7 @@ async fn test_optimize_parallel() {
     study
         .optimize_parallel(20, 4, |mut trial| async move {
             let x = trial.suggest_float("x", -10.0, 10.0)?;
-            Ok::<_, TpeError>((trial, x * x))
+            Ok::<_, Error>((trial, x * x))
         })
         .await
         .expect("parallel optimization should succeed");
@@ -79,7 +79,7 @@ async fn test_optimize_parallel_with_sampler() {
         .optimize_parallel_with_sampler(15, 3, |mut trial| async move {
             let x = trial.suggest_float("x", -5.0, 5.0)?;
             let y = trial.suggest_float("y", -5.0, 5.0)?;
-            Ok::<_, TpeError>((trial, x * x + y * y))
+            Ok::<_, Error>((trial, x * x + y * y))
         })
         .await
         .expect("parallel optimization with sampler should succeed");
@@ -99,7 +99,7 @@ async fn test_optimize_async_all_failures() {
         .await;
 
     assert!(
-        matches!(result, Err(TpeError::NoCompletedTrials)),
+        matches!(result, Err(Error::NoCompletedTrials)),
         "should return NoCompletedTrials when all trials fail"
     );
 }
@@ -116,7 +116,7 @@ async fn test_optimize_async_with_sampler_all_failures() {
         .await;
 
     assert!(
-        matches!(result, Err(TpeError::NoCompletedTrials)),
+        matches!(result, Err(Error::NoCompletedTrials)),
         "should return NoCompletedTrials when all trials fail"
     );
 }
@@ -133,7 +133,7 @@ async fn test_optimize_parallel_all_failures() {
         .await;
 
     assert!(
-        matches!(result, Err(TpeError::NoCompletedTrials)),
+        matches!(result, Err(Error::NoCompletedTrials)),
         "should return NoCompletedTrials when all trials fail"
     );
 }
@@ -150,7 +150,7 @@ async fn test_optimize_parallel_with_sampler_all_failures() {
         .await;
 
     assert!(
-        matches!(result, Err(TpeError::NoCompletedTrials)),
+        matches!(result, Err(Error::NoCompletedTrials)),
         "should return NoCompletedTrials when all trials fail"
     );
 }
@@ -168,9 +168,9 @@ async fn test_optimize_async_partial_failures() {
             async move {
                 if count.is_multiple_of(2) {
                     let x = trial.suggest_float("x", 0.0, 10.0)?;
-                    Ok::<_, TpeError>((trial, x))
+                    Ok::<_, Error>((trial, x))
                 } else {
-                    Err(TpeError::NoCompletedTrials) // Use as error type
+                    Err(Error::NoCompletedTrials) // Use as error type
                 }
             }
         })
@@ -190,7 +190,7 @@ async fn test_optimize_parallel_high_concurrency() {
     study
         .optimize_parallel(5, 10, |mut trial| async move {
             let x = trial.suggest_float("x", 0.0, 10.0)?;
-            Ok::<_, TpeError>((trial, x))
+            Ok::<_, Error>((trial, x))
         })
         .await
         .expect("should handle high concurrency");
@@ -207,7 +207,7 @@ async fn test_optimize_parallel_single_concurrency() {
     study
         .optimize_parallel(10, 1, |mut trial| async move {
             let x = trial.suggest_float("x", 0.0, 10.0)?;
-            Ok::<_, TpeError>((trial, x))
+            Ok::<_, Error>((trial, x))
         })
         .await
         .expect("should work with single concurrency");

tests/integration.rs

@@ -8,7 +8,7 @@
 
 use optimizer::sampler::random::RandomSampler;
 use optimizer::sampler::tpe::TpeSampler;
-use optimizer::{Direction, Study, TpeError, Trial};
+use optimizer::{Direction, Error, Study, Trial};
 
 // =============================================================================
 // Test: optimize simple quadratic function with TPE, finds near-optimal
@@ -30,7 +30,7 @@ fn test_tpe_optimizes_quadratic_function() {
     study
         .optimize_with_sampler(50, |trial| {
             let x = trial.suggest_float("x", -10.0, 10.0)?;
-            Ok::<_, TpeError>((x - 3.0).powi(2))
+            Ok::<_, Error>((x - 3.0).powi(2))
         })
         .expect("optimization should succeed");
 
@@ -61,7 +61,7 @@ fn test_tpe_optimizes_multivariate_function() {
         .optimize_with_sampler(100, |trial| {
             let x = trial.suggest_float("x", -5.0, 5.0)?;
             let y = trial.suggest_float("y", -5.0, 5.0)?;
-            Ok::<_, TpeError>(x * x + y * y)
+            Ok::<_, Error>(x * x + y * y)
         })
         .expect("optimization should succeed");
 
@@ -90,7 +90,7 @@ fn test_tpe_maximization() {
     study
         .optimize_with_sampler(50, |trial| {
             let x = trial.suggest_float("x", -10.0, 10.0)?;
-            Ok::<_, TpeError>(-(x - 2.0).powi(2) + 10.0)
+            Ok::<_, Error>(-(x - 2.0).powi(2) + 10.0)
         })
         .expect("optimization should succeed");
 
@@ -123,7 +123,7 @@ fn test_random_sampler_uniform_float_distribution() {
         .optimize(n_samples, |trial| {
             let x = trial.suggest_float("x", 0.0, 1.0)?;
             samples.push(x);
-            Ok::<_, TpeError>(x)
+            Ok::<_, Error>(x)
         })
         .unwrap();
 
@@ -152,7 +152,7 @@ fn test_random_sampler_uniform_float_distribution() {
 fn test_random_sampler_uniform_int_distribution() {
     let study: Study<f64> = Study::with_sampler(Direction::Minimize, RandomSampler::with_seed(123));
 
-    let n_samples = 1000;
+    let n_samples = 5000;
     let mut counts = [0u32; 10]; // counts for values 1-10
 
     study
@@ -160,16 +160,18 @@ fn test_random_sampler_uniform_int_distribution() {
             let n = trial.suggest_int("n", 1, 10)?;
             assert!((1..=10).contains(&n), "sample {n} out of range [1, 10]");
             counts[(n - 1) as usize] += 1;
-            Ok::<_, TpeError>(n as f64)
+            Ok::<_, Error>(n as f64)
         })
         .unwrap();
 
     // Each value should appear roughly n_samples / 10 times
+    // With 5000 samples, expected ~500 per bucket, std dev ~21
+    // 20% tolerance allows for ~4.5 std devs which is very safe
     let expected = n_samples as f64 / 10.0;
     for (i, &count) in counts.iter().enumerate() {
         let diff = (count as f64 - expected).abs() / expected;
         assert!(
-            diff < 0.3,
+            diff < 0.2,
             "value {} appeared {} times, expected ~{}, diff = {:.1}%",
             i + 1,
             count,
@@ -183,7 +185,7 @@ fn test_random_sampler_uniform_int_distribution() {
 fn test_random_sampler_uniform_categorical_distribution() {
     let study: Study<f64> = Study::with_sampler(Direction::Minimize, RandomSampler::with_seed(456));
 
-    let n_samples = 1000;
+    let n_samples = 2000;
     let mut counts = [0u32; 4];
     let choices = ["a", "b", "c", "d"];
 
@@ -192,16 +194,18 @@ fn test_random_sampler_uniform_categorical_distribution() {
             let choice = trial.suggest_categorical("cat", &choices)?;
             let idx = choices.iter().position(|&c| c == choice).unwrap();
             counts[idx] += 1;
-            Ok::<_, TpeError>(idx as f64)
+            Ok::<_, Error>(idx as f64)
         })
         .unwrap();
 
     // Each category should appear roughly n_samples / 4 times
+    // With 2000 samples, expected ~500 per bucket, std dev ~19
+    // 15% tolerance allows for ~4 std devs which is very safe
     let expected = n_samples as f64 / 4.0;
     for (i, &count) in counts.iter().enumerate() {
         let diff = (count as f64 - expected).abs() / expected;
         assert!(
-            diff < 0.25,
+            diff < 0.15,
             "category {} appeared {} times, expected ~{}, diff = {:.1}%",
             i,
             count,
@@ -227,7 +231,7 @@ fn test_random_sampler_reproducibility() {
         .optimize_with_sampler(100, |trial| {
             let x = trial.suggest_float("x", 0.0, 100.0)?;
             values1.push(x);
-            Ok::<_, TpeError>(x)
+            Ok::<_, Error>(x)
         })
         .unwrap();
 
@@ -235,7 +239,7 @@ fn test_random_sampler_reproducibility() {
         .optimize_with_sampler(100, |trial| {
             let x = trial.suggest_float("x", 0.0, 100.0)?;
             values2.push(x);
-            Ok::<_, TpeError>(x)
+            Ok::<_, Error>(x)
         })
         .unwrap();
 
@@ -367,7 +371,7 @@ fn test_parameter_conflict_float_different_bounds() {
     trial.suggest_float("x", 0.0, 1.0).unwrap();
     let result = trial.suggest_float("x", 0.0, 2.0); // Different upper bound
 
-    assert!(matches!(result, Err(TpeError::ParameterConflict { .. })));
+    assert!(matches!(result, Err(Error::ParameterConflict { .. })));
 }
 
 #[test]
@@ -377,7 +381,7 @@ fn test_parameter_conflict_float_vs_log() {
     trial.suggest_float("x", 0.1, 1.0).unwrap();
     let result = trial.suggest_float_log("x", 0.1, 1.0); // Same bounds but log scale
 
-    assert!(matches!(result, Err(TpeError::ParameterConflict { .. })));
+    assert!(matches!(result, Err(Error::ParameterConflict { .. })));
 }
 
 #[test]
@@ -387,7 +391,7 @@ fn test_parameter_conflict_float_vs_step() {
     trial.suggest_float("x", 0.0, 1.0).unwrap();
     let result = trial.suggest_float_step("x", 0.0, 1.0, 0.1); // Same bounds but with step
 
-    assert!(matches!(result, Err(TpeError::ParameterConflict { .. })));
+    assert!(matches!(result, Err(Error::ParameterConflict { .. })));
 }
 
 #[test]
@@ -397,7 +401,7 @@ fn test_parameter_conflict_int_different_bounds() {
     trial.suggest_int("n", 1, 10).unwrap();
     let result = trial.suggest_int("n", 1, 20); // Different upper bound
 
-    assert!(matches!(result, Err(TpeError::ParameterConflict { .. })));
+    assert!(matches!(result, Err(Error::ParameterConflict { .. })));
 }
 
 #[test]
@@ -407,7 +411,7 @@ fn test_parameter_conflict_int_vs_log() {
     trial.suggest_int("n", 1, 100).unwrap();
     let result = trial.suggest_int_log("n", 1, 100); // Same bounds but log scale
 
-    assert!(matches!(result, Err(TpeError::ParameterConflict { .. })));
+    assert!(matches!(result, Err(Error::ParameterConflict { .. })));
 }
 
 #[test]
@@ -417,7 +421,7 @@ fn test_parameter_conflict_categorical_different_n_choices() {
     trial.suggest_categorical("opt", &["a", "b", "c"]).unwrap();
     let result = trial.suggest_categorical("opt", &["x", "y"]); // Different number of choices
 
-    assert!(matches!(result, Err(TpeError::ParameterConflict { .. })));
+    assert!(matches!(result, Err(Error::ParameterConflict { .. })));
 }
 
 #[test]
@@ -427,7 +431,7 @@ fn test_parameter_conflict_float_vs_int() {
     trial.suggest_float("x", 0.0, 10.0).unwrap();
     let result = trial.suggest_int("x", 0, 10); // Different type
 
-    assert!(matches!(result, Err(TpeError::ParameterConflict { .. })));
+    assert!(matches!(result, Err(Error::ParameterConflict { .. })));
 }
 
 #[test]
@@ -438,7 +442,7 @@ fn test_parameter_conflict_returns_name() {
     let result = trial.suggest_float("my_param", 0.0, 2.0);
 
     match result {
-        Err(TpeError::ParameterConflict { name, .. }) => {
+        Err(Error::ParameterConflict { name, .. }) => {
             assert_eq!(name, "my_param");
         }
         _ => panic!("expected ParameterConflict error"),
@@ -456,7 +460,7 @@ fn test_empty_categorical_returns_error() {
 
     let result = trial.suggest_categorical("opt", empty);
 
-    assert!(matches!(result, Err(TpeError::EmptyChoices)));
+    assert!(matches!(result, Err(Error::EmptyChoices)));
 }
 
 #[test]
@@ -466,7 +470,7 @@ fn test_empty_categorical_vec_returns_error() {
 
     let result = trial.suggest_categorical("numbers", &empty);
 
-    assert!(matches!(result, Err(TpeError::EmptyChoices)));
+    assert!(matches!(result, Err(Error::EmptyChoices)));
 }
 
 // =============================================================================
@@ -480,7 +484,7 @@ fn test_study_basic_workflow() {
     study
         .optimize(10, |trial| {
             let x = trial.suggest_float("x", -5.0, 5.0)?;
-            Ok::<_, TpeError>(x * x)
+            Ok::<_, Error>(x * x)
         })
         .expect("optimization should succeed");
 
@@ -517,7 +521,7 @@ fn test_no_completed_trials_error() {
     let study: Study<f64> = Study::new(Direction::Minimize);
 
     let result = study.best_trial();
-    assert!(matches!(result, Err(TpeError::NoCompletedTrials)));
+    assert!(matches!(result, Err(Error::NoCompletedTrials)));
 }
 
 #[test]
@@ -526,11 +530,11 @@ fn test_invalid_bounds_errors() {
 
     // low > high for float
     let result = trial.suggest_float("x", 10.0, 5.0);
-    assert!(matches!(result, Err(TpeError::InvalidBounds { .. })));
+    assert!(matches!(result, Err(Error::InvalidBounds { .. })));
 
     // low > high for int
     let result = trial.suggest_int("n", 100, 50);
-    assert!(matches!(result, Err(TpeError::InvalidBounds { .. })));
+    assert!(matches!(result, Err(Error::InvalidBounds { .. })));
 }
 
 #[test]
@@ -539,14 +543,14 @@ fn test_invalid_log_bounds_errors() {
 
     // low <= 0 for log float
     let result = trial.suggest_float_log("x", 0.0, 1.0);
-    assert!(matches!(result, Err(TpeError::InvalidLogBounds)));
+    assert!(matches!(result, Err(Error::InvalidLogBounds)));
 
     let result = trial.suggest_float_log("y", -1.0, 1.0);
-    assert!(matches!(result, Err(TpeError::InvalidLogBounds)));
+    assert!(matches!(result, Err(Error::InvalidLogBounds)));
 
     // low < 1 for log int
     let result = trial.suggest_int_log("n", 0, 100);
-    assert!(matches!(result, Err(TpeError::InvalidLogBounds)));
+    assert!(matches!(result, Err(Error::InvalidLogBounds)));
 }
 
 #[test]
@@ -555,14 +559,14 @@ fn test_invalid_step_errors() {
 
     // step <= 0 for float
     let result = trial.suggest_float_step("x", 0.0, 1.0, 0.0);
-    assert!(matches!(result, Err(TpeError::InvalidStep)));
+    assert!(matches!(result, Err(Error::InvalidStep)));
 
     let result = trial.suggest_float_step("y", 0.0, 1.0, -0.1);
-    assert!(matches!(result, Err(TpeError::InvalidStep)));
+    assert!(matches!(result, Err(Error::InvalidStep)));
 
     // step <= 0 for int
     let result = trial.suggest_int_step("n", 0, 100, 0);
-    assert!(matches!(result, Err(TpeError::InvalidStep)));
+    assert!(matches!(result, Err(Error::InvalidStep)));
 }
 
 #[test]
@@ -588,7 +592,7 @@ fn test_tpe_with_categorical_parameter() {
                 "cubic" => -((x - 1.0).powi(2)) + 10.0, // peak at x=1, max value 10
                 _ => unreachable!(),
             };
-            Ok::<_, TpeError>(value)
+            Ok::<_, Error>(value)
         })
         .expect("optimization should succeed");
 
@@ -615,7 +619,7 @@ fn test_tpe_with_integer_parameters() {
     study
         .optimize_with_sampler(30, |trial| {
             let n = trial.suggest_int("n", 1, 10)?;
-            Ok::<_, TpeError>(((n - 7) as f64).powi(2))
+            Ok::<_, Error>(((n - 7) as f64).powi(2))
         })
         .expect("optimization should succeed");
 
@@ -643,7 +647,7 @@ fn test_callback_early_stopping() {
             |trial| {
                 trials_run.set(trials_run.get() + 1);
                 let x = trial.suggest_float("x", 0.0, 10.0)?;
-                Ok::<_, TpeError>(x)
+                Ok::<_, Error>(x)
             },
             |_study, _trial| {
                 // Stop after 5 trials
@@ -666,7 +670,7 @@ fn test_study_trials_iteration() {
     study
         .optimize(5, |trial| {
             let x = trial.suggest_float("x", 0.0, 1.0)?;
-            Ok::<_, TpeError>(x)
+            Ok::<_, Error>(x)
         })
         .unwrap();
 
@@ -758,7 +762,7 @@ fn test_best_value() {
     study
         .optimize(10, |trial| {
             let x = trial.suggest_float("x", 0.0, 10.0)?;
-            Ok::<_, TpeError>(x)
+            Ok::<_, Error>(x)
         })
         .unwrap();
 
@@ -792,7 +796,7 @@ fn test_study_set_sampler() {
     study
         .optimize_with_sampler(10, |trial| {
             let x = trial.suggest_float("x", -5.0, 5.0)?;
-            Ok::<_, TpeError>(x * x)
+            Ok::<_, Error>(x * x)
         })
         .expect("optimization should succeed with new sampler");
 
@@ -807,7 +811,7 @@ fn test_study_with_i32_value_type() {
     study
         .optimize(10, |trial| {
             let x = trial.suggest_int("x", -10, 10)?;
-            Ok::<_, TpeError>(x.abs() as i32)
+            Ok::<_, Error>(x.abs() as i32)
         })
         .expect("optimization should succeed");
 
@@ -824,7 +828,7 @@ fn test_optimize_all_trials_fail() {
     let result = study.optimize(5, |_trial| Err::<f64, &str>("always fails"));
 
     assert!(
-        matches!(result, Err(TpeError::NoCompletedTrials)),
+        matches!(result, Err(Error::NoCompletedTrials)),
         "should return NoCompletedTrials when all trials fail"
     );
 }
@@ -842,7 +846,7 @@ fn test_optimize_with_callback_all_trials_fail() {
     );
 
     assert!(
-        matches!(result, Err(TpeError::NoCompletedTrials)),
+        matches!(result, Err(Error::NoCompletedTrials)),
         "should return NoCompletedTrials when all trials fail"
     );
 }
@@ -854,7 +858,7 @@ fn test_optimize_with_sampler_all_trials_fail() {
     let result = study.optimize_with_sampler(5, |_trial| Err::<f64, &str>("always fails"));
 
     assert!(
-        matches!(result, Err(TpeError::NoCompletedTrials)),
+        matches!(result, Err(Error::NoCompletedTrials)),
         "should return NoCompletedTrials when all trials fail"
     );
 }
@@ -872,7 +876,7 @@ fn test_optimize_with_callback_sampler_all_trials_fail() {
     );
 
     assert!(
-        matches!(result, Err(TpeError::NoCompletedTrials)),
+        matches!(result, Err(Error::NoCompletedTrials)),
         "should return NoCompletedTrials when all trials fail"
     );
 }
@@ -882,7 +886,7 @@ fn test_trial_debug_format() {
     let mut trial = Trial::new(42);
     trial.suggest_float("x", 0.0, 1.0).unwrap();
 
-    let debug_str = format!("{:?}", trial);
+    let debug_str = format!("{trial:?}");
 
     // Should contain trial id and other fields
     assert!(debug_str.contains("Trial"));
@@ -902,7 +906,7 @@ fn test_tpe_sampler_builder_default_trait() {
     study
         .optimize_with_sampler(5, |trial| {
             let x = trial.suggest_float("x", 0.0, 1.0)?;
-            Ok::<_, TpeError>(x)
+            Ok::<_, Error>(x)
         })
         .unwrap();
 
@@ -917,7 +921,7 @@ fn test_tpe_sampler_default_trait() {
     study
         .optimize_with_sampler(5, |trial| {
             let x = trial.suggest_float("x", 0.0, 1.0)?;
-            Ok::<_, TpeError>(x)
+            Ok::<_, Error>(x)
         })
         .unwrap();
 
@@ -938,7 +942,7 @@ fn test_tpe_with_fixed_kde_bandwidth() {
     study
         .optimize_with_sampler(20, |trial| {
             let x = trial.suggest_float("x", -5.0, 5.0)?;
-            Ok::<_, TpeError>(x * x)
+            Ok::<_, Error>(x * x)
         })
         .expect("optimization should succeed");
 
@@ -949,7 +953,7 @@ fn test_tpe_with_fixed_kde_bandwidth() {
 #[test]
 fn test_tpe_sampler_invalid_kde_bandwidth() {
     let result = TpeSampler::with_config(0.25, 10, 24, Some(-1.0), None);
-    assert!(matches!(result, Err(TpeError::InvalidBandwidth(_))));
+    assert!(matches!(result, Err(Error::InvalidBandwidth(_))));
 }
 
 #[test]
@@ -966,7 +970,7 @@ fn test_tpe_split_trials_with_two_trials() {
     study
         .optimize_with_sampler(5, |trial| {
             let x = trial.suggest_float("x", 0.0, 10.0)?;
-            Ok::<_, TpeError>(x)
+            Ok::<_, Error>(x)
         })
         .expect("optimization should succeed with small history");
 
@@ -987,7 +991,7 @@ fn test_tpe_with_log_scale_int() {
         .optimize_with_sampler(20, |trial| {
             let batch_size = trial.suggest_int_log("batch_size", 1, 1024)?;
             // Optimal around batch_size = 32
-            Ok::<_, TpeError>(((batch_size as f64).log2() - 5.0).powi(2))
+            Ok::<_, Error>(((batch_size as f64).log2() - 5.0).powi(2))
         })
         .expect("optimization should succeed");
 
@@ -1009,7 +1013,7 @@ fn test_tpe_with_step_distributions() {
         .optimize_with_sampler(20, |trial| {
             let x = trial.suggest_float_step("x", 0.0, 10.0, 0.5)?;
             let n = trial.suggest_int_step("n", 0, 100, 10)?;
-            Ok::<_, TpeError>((x - 5.0).powi(2) + ((n - 50) as f64).powi(2))
+            Ok::<_, Error>((x - 5.0).powi(2) + ((n - 50) as f64).powi(2))
         })
         .expect("optimization should succeed");
 
@@ -1088,7 +1092,7 @@ fn test_tpe_empty_good_or_bad_values_fallback() {
     study
         .optimize_with_sampler(10, |trial| {
             let x = trial.suggest_float("x", 0.0, 10.0)?;
-            Ok::<_, TpeError>(x)
+            Ok::<_, Error>(x)
         })
         .unwrap();
 
@@ -1096,7 +1100,7 @@ fn test_tpe_empty_good_or_bad_values_fallback() {
     study
         .optimize_with_sampler(5, |trial| {
             let y = trial.suggest_float("y", 0.0, 10.0)?;
-            Ok::<_, TpeError>(y)
+            Ok::<_, Error>(y)
         })
         .unwrap();
 
@@ -1114,7 +1118,7 @@ fn test_callback_early_stopping_on_first_trial() {
             100,
             |trial| {
                 let x = trial.suggest_float("x", 0.0, 10.0)?;
-                Ok::<_, TpeError>(x)
+                Ok::<_, Error>(x)
             },
             |_study, _trial| {
                 // Stop immediately after first trial
@@ -1138,7 +1142,7 @@ fn test_callback_sampler_early_stopping() {
             100,
             |trial| {
                 let x = trial.suggest_float("x", 0.0, 10.0)?;
-                Ok::<_, TpeError>(x)
+                Ok::<_, Error>(x)
             },
             |study, _trial| {
                 if study.n_trials() >= 3 {
@@ -1174,7 +1178,7 @@ fn test_best_trial_with_nan_values() {
     study
         .optimize(5, |trial| {
             let x = trial.suggest_float("x", 0.0, 10.0)?;
-            Ok::<_, TpeError>(x)
+            Ok::<_, Error>(x)
         })
         .unwrap();
 
@@ -1182,3 +1186,223 @@ fn test_best_trial_with_nan_values() {
     let best = study.best_trial();
     assert!(best.is_ok());
 }
+
+// =============================================================================
+// Tests for suggest_bool
+// =============================================================================
+
+#[test]
+fn test_suggest_bool_caching() {
+    let mut trial = Trial::new(0);
+
+    let b1 = trial.suggest_bool("flag").unwrap();
+    let b2 = trial.suggest_bool("flag").unwrap();
+
+    assert_eq!(b1, b2, "repeated suggest_bool should return cached value");
+}
+
+#[test]
+fn test_suggest_bool_multiple_parameters() {
+    let mut trial = Trial::new(0);
+
+    let a = trial.suggest_bool("use_dropout").unwrap();
+    let b = trial.suggest_bool("use_batchnorm").unwrap();
+    let c = trial.suggest_bool("use_skip_connections").unwrap();
+
+    // All should be cached independently
+    assert_eq!(a, trial.suggest_bool("use_dropout").unwrap());
+    assert_eq!(b, trial.suggest_bool("use_batchnorm").unwrap());
+    assert_eq!(c, trial.suggest_bool("use_skip_connections").unwrap());
+}
+
+#[test]
+fn test_suggest_bool_in_optimization() {
+    let study: Study<f64> = Study::new(Direction::Minimize);
+
+    study
+        .optimize(10, |trial| {
+            let use_feature = trial.suggest_bool("use_feature")?;
+            let x = trial.suggest_float("x", 0.0, 10.0)?;
+
+            // Objective depends on boolean flag
+            let value = if use_feature { x } else { x * 2.0 };
+            Ok::<_, Error>(value)
+        })
+        .unwrap();
+
+    assert_eq!(study.n_trials(), 10);
+}
+
+#[test]
+fn test_suggest_bool_with_tpe() {
+    let sampler = TpeSampler::builder()
+        .seed(42)
+        .n_startup_trials(5)
+        .build()
+        .unwrap();
+
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+
+    study
+        .optimize_with_sampler(20, |trial| {
+            let use_large = trial.suggest_bool("use_large")?;
+            let base = if use_large { 10.0 } else { 1.0 };
+            let x = trial.suggest_float("x", 0.0, base)?;
+            Ok::<_, Error>(x)
+        })
+        .unwrap();
+
+    let best = study.best_trial().unwrap();
+    // Best should prefer use_large=false for smaller range
+    assert!(best.value < 5.0);
+}
+
+// =============================================================================
+// Tests for suggest_range
+// =============================================================================
+
+#[test]
+fn test_suggest_range_float_exclusive() {
+    let mut trial = Trial::new(0);
+
+    let x = trial.suggest_range("x", 0.0..1.0).unwrap();
+    assert!((0.0..=1.0).contains(&x), "value {x} out of range 0.0..1.0");
+}
+
+#[test]
+fn test_suggest_range_float_inclusive() {
+    let mut trial = Trial::new(0);
+
+    let x = trial.suggest_range("x", 0.0..=1.0).unwrap();
+    assert!((0.0..=1.0).contains(&x), "value {x} out of range 0.0..=1.0");
+}
+
+#[test]
+fn test_suggest_range_int_exclusive() {
+    let mut trial = Trial::new(0);
+
+    // 1..10 means 1 to 9 inclusive
+    let n = trial.suggest_range("n", 1_i64..10).unwrap();
+    assert!(
+        (1..=9).contains(&n),
+        "value {n} out of range 1..10 (should be 1-9)"
+    );
+}
+
+#[test]
+fn test_suggest_range_int_inclusive() {
+    let mut trial = Trial::new(0);
+
+    // 1..=10 means 1 to 10 inclusive
+    let n = trial.suggest_range("n", 1_i64..=10).unwrap();
+    assert!(
+        (1..=10).contains(&n),
+        "value {n} out of range 1..=10 (should be 1-10)"
+    );
+}
+
+#[test]
+fn test_suggest_range_caching_float() {
+    let mut trial = Trial::new(0);
+
+    let x1 = trial.suggest_range("x", 0.0..1.0).unwrap();
+    let x2 = trial.suggest_range("x", 0.0..1.0).unwrap();
+
+    assert_eq!(x1, x2, "repeated suggest_range should return cached value");
+}
+
+#[test]
+fn test_suggest_range_caching_int() {
+    let mut trial = Trial::new(0);
+
+    let n1 = trial.suggest_range("n", 1_i64..=100).unwrap();
+    let n2 = trial.suggest_range("n", 1_i64..=100).unwrap();
+
+    assert_eq!(n1, n2, "repeated suggest_range should return cached value");
+}
+
+#[test]
+fn test_suggest_range_multiple_parameters() {
+    let mut trial = Trial::new(0);
+
+    let x = trial.suggest_range("x", 0.0..1.0).unwrap();
+    let y = trial.suggest_range("y", -5.0..=5.0).unwrap();
+    let n = trial.suggest_range("n", 1_i64..10).unwrap();
+    let m = trial.suggest_range("m", 100_i64..=200).unwrap();
+
+    // All should be cached independently
+    assert_eq!(x, trial.suggest_range("x", 0.0..1.0).unwrap());
+    assert_eq!(y, trial.suggest_range("y", -5.0..=5.0).unwrap());
+    assert_eq!(n, trial.suggest_range("n", 1_i64..10).unwrap());
+    assert_eq!(m, trial.suggest_range("m", 100_i64..=200).unwrap());
+}
+
+#[test]
+fn test_suggest_range_in_optimization() {
+    let study: Study<f64> = Study::new(Direction::Minimize);
+
+    study
+        .optimize(10, |trial| {
+            let x = trial.suggest_range("x", -10.0..10.0)?;
+            let n = trial.suggest_range("n", 1_i64..=5)?;
+            Ok::<_, Error>(x * x + n as f64)
+        })
+        .unwrap();
+
+    assert_eq!(study.n_trials(), 10);
+}
+
+#[test]
+fn test_suggest_range_with_tpe() {
+    let sampler = TpeSampler::builder()
+        .seed(42)
+        .n_startup_trials(5)
+        .build()
+        .unwrap();
+
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+
+    study
+        .optimize_with_sampler(30, |trial| {
+            let x = trial.suggest_range("x", -5.0..=5.0)?;
+            let n = trial.suggest_range("n", 1_i64..=10)?;
+            Ok::<_, Error>(x * x + (n as f64 - 5.0).powi(2))
+        })
+        .unwrap();
+
+    let best = study.best_trial().unwrap();
+    // TPE should find near-optimal solution
+    assert!(best.value < 10.0, "TPE should find good solution");
+}
+
+#[test]
+fn test_suggest_range_empty_int_range_error() {
+    let mut trial = Trial::new(0);
+
+    // 5..5 is empty (no valid integers)
+    let result = trial.suggest_range("n", 5_i64..5);
+    assert!(
+        matches!(result, Err(Error::InvalidBounds { .. })),
+        "empty range should return InvalidBounds error"
+    );
+}
+
+#[test]
+fn test_suggest_range_single_value_int() {
+    let mut trial = Trial::new(0);
+
+    // 5..=5 has exactly one value: 5
+    let n = trial.suggest_range("n", 5_i64..=5).unwrap();
+    assert_eq!(n, 5, "single-value range should return that value");
+}
+
+#[test]
+fn test_suggest_range_single_value_float() {
+    let mut trial = Trial::new(0);
+
+    let x = trial.suggest_range("x", 4.2..=4.2).unwrap();
+    assert!(
+        (x - 4.2).abs() < f64::EPSILON,
+        "single-value range should return that value"
+    );
+}

tests/multivariate_tpe_integration.rs

@@ -0,0 +1,393 @@
+//! Integration tests for the Multivariate TPE sampler.
+//!
+//! These tests compare the performance of `MultivariateTpeSampler` against
+//! the standard `TpeSampler` on problems with and without parameter correlations.
+
+#![allow(
+    clippy::cast_sign_loss,
+    clippy::cast_precision_loss,
+    clippy::cast_possible_truncation
+)]
+
+use optimizer::sampler::MultivariateTpeSampler;
+use optimizer::sampler::tpe::TpeSampler;
+use optimizer::{Direction, Error, Study};
+
+// =============================================================================
+// Rosenbrock function: f(x,y) = (a-x)^2 + b*(y-x^2)^2
+// This is a classic benchmark with strong parameter correlation.
+// Optimal: (x, y) = (a, a^2) with f(x, y) = 0
+// Standard parameters: a = 1, b = 100
+// The "banana-shaped" valley makes this hard for independent samplers.
+// =============================================================================
+
+/// Computes the Rosenbrock function value.
+///
+/// f(x, y) = (a - x)^2 + b * (y - x^2)^2
+///
+/// With standard parameters a = 1, b = 100:
+/// - Optimal point: (1, 1)
+/// - Optimal value: 0
+fn rosenbrock(x: f64, y: f64) -> f64 {
+    let a = 1.0;
+    let b = 100.0;
+    (a - x).powi(2) + b * (y - x * x).powi(2)
+}
+
+// =============================================================================
+// Test: Multivariate TPE on Rosenbrock function (correlated parameters)
+// =============================================================================
+
+#[test]
+fn test_multivariate_tpe_rosenbrock_finds_good_solution() {
+    // Multivariate TPE should find a good solution on Rosenbrock
+    // because it can model the correlation between x and y
+    let sampler = MultivariateTpeSampler::builder()
+        .seed(42)
+        .n_startup_trials(10)
+        .n_ei_candidates(24)
+        .build()
+        .unwrap();
+
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+
+    study
+        .optimize_with_sampler(100, |trial| {
+            let x = trial.suggest_float("x", -2.0, 2.0)?;
+            let y = trial.suggest_float("y", -2.0, 4.0)?;
+            Ok::<_, Error>(rosenbrock(x, y))
+        })
+        .expect("optimization should succeed");
+
+    let best = study.best_trial().expect("should have at least one trial");
+
+    // Multivariate TPE should find a reasonably good solution
+    // The global minimum is 0, but getting close is challenging
+    assert!(
+        best.value < 10.0,
+        "Multivariate TPE should find good Rosenbrock solution: best value {} should be < 10.0",
+        best.value
+    );
+}
+
+#[test]
+fn test_independent_tpe_rosenbrock() {
+    // Independent TPE (standard TpeSampler) on Rosenbrock
+    // This establishes a baseline for comparison
+    let sampler = TpeSampler::builder()
+        .seed(42)
+        .n_startup_trials(10)
+        .n_ei_candidates(24)
+        .build()
+        .unwrap();
+
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+
+    study
+        .optimize_with_sampler(100, |trial| {
+            let x = trial.suggest_float("x", -2.0, 2.0)?;
+            let y = trial.suggest_float("y", -2.0, 4.0)?;
+            Ok::<_, Error>(rosenbrock(x, y))
+        })
+        .expect("optimization should succeed");
+
+    let best = study.best_trial().expect("should have at least one trial");
+
+    // Independent TPE should still find a decent solution,
+    // but may not be as good as multivariate TPE on this correlated problem
+    assert!(
+        best.value < 50.0,
+        "Independent TPE should find reasonable Rosenbrock solution: best value {} should be < 50.0",
+        best.value
+    );
+}
+
+#[test]
+fn test_multivariate_tpe_outperforms_on_correlated_problem() {
+    // Run multiple seeds and compare average performance
+    // Multivariate TPE should generally find better solutions on Rosenbrock
+    let n_runs = 5;
+    let n_trials = 80;
+
+    let mut multivariate_best_values = Vec::new();
+    let mut independent_best_values = Vec::new();
+
+    for seed in 0..n_runs {
+        // Multivariate TPE
+        let multivariate_sampler = MultivariateTpeSampler::builder()
+            .seed(seed as u64)
+            .n_startup_trials(10)
+            .n_ei_candidates(24)
+            .build()
+            .unwrap();
+
+        let study: Study<f64> = Study::with_sampler(Direction::Minimize, multivariate_sampler);
+
+        study
+            .optimize_with_sampler(n_trials, |trial| {
+                let x = trial.suggest_float("x", -2.0, 2.0)?;
+                let y = trial.suggest_float("y", -2.0, 4.0)?;
+                Ok::<_, Error>(rosenbrock(x, y))
+            })
+            .unwrap();
+
+        multivariate_best_values.push(study.best_trial().unwrap().value);
+
+        // Independent TPE
+        let independent_sampler = TpeSampler::builder()
+            .seed(seed as u64)
+            .n_startup_trials(10)
+            .n_ei_candidates(24)
+            .build()
+            .unwrap();
+
+        let study: Study<f64> = Study::with_sampler(Direction::Minimize, independent_sampler);
+
+        study
+            .optimize_with_sampler(n_trials, |trial| {
+                let x = trial.suggest_float("x", -2.0, 2.0)?;
+                let y = trial.suggest_float("y", -2.0, 4.0)?;
+                Ok::<_, Error>(rosenbrock(x, y))
+            })
+            .unwrap();
+
+        independent_best_values.push(study.best_trial().unwrap().value);
+    }
+
+    let multivariate_mean: f64 = multivariate_best_values.iter().sum::<f64>() / n_runs as f64;
+    let independent_mean: f64 = independent_best_values.iter().sum::<f64>() / n_runs as f64;
+
+    // Log results for debugging (these won't show in normal test runs,
+    // but are useful when running with --nocapture)
+    eprintln!("Multivariate TPE mean best: {multivariate_mean:.4}");
+    eprintln!("Independent TPE mean best: {independent_mean:.4}");
+    eprintln!("Multivariate best values: {multivariate_best_values:?}");
+    eprintln!("Independent best values: {independent_best_values:?}");
+
+    // Both methods should find reasonable solutions
+    assert!(
+        multivariate_mean < 20.0,
+        "Multivariate TPE mean {multivariate_mean:.4} should be < 20.0"
+    );
+    assert!(
+        independent_mean < 100.0,
+        "Independent TPE mean {independent_mean:.4} should be < 100.0"
+    );
+}
+
+// =============================================================================
+// Independent parameter problem: f(x,y) = x^2 + y^2
+// No correlation between parameters - both methods should work equally well.
+// =============================================================================
+
+/// Simple sphere function with independent parameters.
+///
+/// f(x, y) = x^2 + y^2
+///
+/// Optimal point: (0, 0)
+/// Optimal value: 0
+fn sphere(x: f64, y: f64) -> f64 {
+    x * x + y * y
+}
+
+#[test]
+fn test_multivariate_tpe_independent_problem() {
+    // On an independent problem, multivariate TPE should still work well
+    let sampler = MultivariateTpeSampler::builder()
+        .seed(42)
+        .n_startup_trials(10)
+        .n_ei_candidates(24)
+        .build()
+        .unwrap();
+
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+
+    study
+        .optimize_with_sampler(50, |trial| {
+            let x = trial.suggest_float("x", -5.0, 5.0)?;
+            let y = trial.suggest_float("y", -5.0, 5.0)?;
+            Ok::<_, Error>(sphere(x, y))
+        })
+        .expect("optimization should succeed");
+
+    let best = study.best_trial().expect("should have at least one trial");
+
+    assert!(
+        best.value < 5.0,
+        "Multivariate TPE should find good solution on sphere: best value {} should be < 5.0",
+        best.value
+    );
+}
+
+#[test]
+fn test_independent_tpe_independent_problem() {
+    // Baseline: independent TPE on sphere function
+    let sampler = TpeSampler::builder()
+        .seed(42)
+        .n_startup_trials(10)
+        .n_ei_candidates(24)
+        .build()
+        .unwrap();
+
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+
+    study
+        .optimize_with_sampler(50, |trial| {
+            let x = trial.suggest_float("x", -5.0, 5.0)?;
+            let y = trial.suggest_float("y", -5.0, 5.0)?;
+            Ok::<_, Error>(sphere(x, y))
+        })
+        .expect("optimization should succeed");
+
+    let best = study.best_trial().expect("should have at least one trial");
+
+    assert!(
+        best.value < 5.0,
+        "Independent TPE should find good solution on sphere: best value {} should be < 5.0",
+        best.value
+    );
+}
+
+#[test]
+fn test_both_samplers_work_on_independent_problem() {
+    // Run both samplers on the independent sphere function
+    // and verify they both achieve similar performance
+    let n_runs = 5;
+    let n_trials = 50;
+
+    let mut multivariate_results = Vec::new();
+    let mut independent_results = Vec::new();
+
+    for seed in 0..n_runs {
+        // Multivariate TPE
+        let sampler = MultivariateTpeSampler::builder()
+            .seed(seed as u64)
+            .n_startup_trials(10)
+            .build()
+            .unwrap();
+
+        let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+
+        study
+            .optimize_with_sampler(n_trials, |trial| {
+                let x = trial.suggest_float("x", -5.0, 5.0)?;
+                let y = trial.suggest_float("y", -5.0, 5.0)?;
+                Ok::<_, Error>(sphere(x, y))
+            })
+            .unwrap();
+
+        multivariate_results.push(study.best_trial().unwrap().value);
+
+        // Independent TPE
+        let sampler = TpeSampler::builder()
+            .seed(seed as u64)
+            .n_startup_trials(10)
+            .build()
+            .unwrap();
+
+        let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+
+        study
+            .optimize_with_sampler(n_trials, |trial| {
+                let x = trial.suggest_float("x", -5.0, 5.0)?;
+                let y = trial.suggest_float("y", -5.0, 5.0)?;
+                Ok::<_, Error>(sphere(x, y))
+            })
+            .unwrap();
+
+        independent_results.push(study.best_trial().unwrap().value);
+    }
+
+    let multivariate_mean: f64 = multivariate_results.iter().sum::<f64>() / n_runs as f64;
+    let independent_mean: f64 = independent_results.iter().sum::<f64>() / n_runs as f64;
+
+    eprintln!("Sphere function results:");
+    eprintln!("  Multivariate TPE mean: {multivariate_mean:.4}");
+    eprintln!("  Independent TPE mean: {independent_mean:.4}");
+
+    // Both should find good solutions on this simple problem
+    assert!(
+        multivariate_mean < 5.0,
+        "Multivariate TPE mean {multivariate_mean:.4} should be < 5.0 on sphere"
+    );
+    assert!(
+        independent_mean < 5.0,
+        "Independent TPE mean {independent_mean:.4} should be < 5.0 on sphere"
+    );
+}
+
+// =============================================================================
+// Test: Multivariate TPE with group decomposition
+// =============================================================================
+
+#[test]
+fn test_multivariate_tpe_with_group_decomposition() {
+    // Test that group decomposition works correctly
+    let sampler = MultivariateTpeSampler::builder()
+        .seed(42)
+        .n_startup_trials(10)
+        .group(true) // Enable group decomposition
+        .build()
+        .unwrap();
+
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+
+    study
+        .optimize_with_sampler(50, |trial| {
+            let x = trial.suggest_float("x", -5.0, 5.0)?;
+            let y = trial.suggest_float("y", -5.0, 5.0)?;
+            Ok::<_, Error>(sphere(x, y))
+        })
+        .expect("optimization should succeed");
+
+    let best = study.best_trial().expect("should have at least one trial");
+
+    assert!(
+        best.value < 10.0,
+        "Multivariate TPE with groups should find good solution: best value {} should be < 10.0",
+        best.value
+    );
+}
+
+// =============================================================================
+// Test: Multivariate TPE with mixed parameter types
+// =============================================================================
+
+#[test]
+fn test_multivariate_tpe_mixed_parameter_types() {
+    // Test with float, int, and categorical parameters
+    let sampler = MultivariateTpeSampler::builder()
+        .seed(42)
+        .n_startup_trials(10)
+        .build()
+        .unwrap();
+
+    let study: Study<f64> = Study::with_sampler(Direction::Minimize, sampler);
+
+    study
+        .optimize_with_sampler(50, |trial| {
+            let x = trial.suggest_float("x", -5.0, 5.0)?;
+            let n = trial.suggest_int("n", 1, 10)?;
+            let mode = trial.suggest_categorical("mode", &["a", "b", "c"])?;
+
+            // Objective depends on all parameters
+            let mode_factor = match mode {
+                "a" => 1.0,
+                "b" => 0.5,
+                "c" => 2.0,
+                _ => unreachable!(),
+            };
+
+            Ok::<_, Error>(x * x + (n as f64 - 5.0).powi(2) * mode_factor)
+        })
+        .expect("optimization should succeed");
+
+    let best = study.best_trial().expect("should have at least one trial");
+
+    // Should find a reasonable solution
+    assert!(
+        best.value < 25.0,
+        "Multivariate TPE should handle mixed types: best value {} should be < 25.0",
+        best.value
+    );
+}