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""" |
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CmaEsSampler Example - Covariance Matrix Adaptation Evolution Strategy |
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CMA-ES is a powerful evolution strategy particularly effective for continuous |
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optimization problems. It adapts both the mean and covariance matrix of a |
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multivariate normal distribution to efficiently explore the parameter space. |
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Characteristics: |
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- Excellent for continuous parameter optimization |
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- Adapts search distribution shape and orientation |
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- Self-adaptive step size control |
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- Handles ill-conditioned problems well |
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- Does not work with categorical parameters |
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- Requires 'cmaes' package: pip install cmaes |
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Note: This example includes a fallback if 'cmaes' package is not installed. |
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""" |
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import numpy as np |
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from sklearn.datasets import make_regression |
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from sklearn.neural_network import MLPRegressor |
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from sklearn.model_selection import cross_val_score |
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from sklearn.metrics import mean_squared_error |
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from hyperactive.experiment.integrations import SklearnCvExperiment |
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from hyperactive.opt.optuna import CmaEsSampler |
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def cmaes_theory(): |
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"""Explain CMA-ES algorithm theory.""" |
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# CMA-ES Algorithm Theory: |
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# 1. Maintains a multivariate normal distribution N(μ, σ²C) |
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# - μ: mean vector (center of search) |
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# - σ: step size (global scaling) |
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# - C: covariance matrix (shape and orientation) |
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# |
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# 2. In each generation: |
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# - Sample λ offspring from N(μ, σ²C) |
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# - Evaluate all offspring |
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# - Select μ best solutions |
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# - Update μ, σ, and C based on selected solutions |
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# |
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# 3. Adaptive features: |
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# - Covariance matrix learns correlations between parameters |
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# - Step size adapts to local landscape |
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# - Handles rotated/scaled problems efficiently |
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def main(): |
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# === CmaEsSampler Example === |
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# Covariance Matrix Adaptation Evolution Strategy |
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# Check if cmaes is available |
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try: |
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import cmaes |
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cmaes_available = True |
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print(" CMA-ES package is available") |
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except ImportError: |
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cmaes_available = False |
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print("⚠ CMA-ES package not available. Install with: pip install cmaes") |
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print(" This example will demonstrate the interface but may fail at runtime.") |
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print() |
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cmaes_theory() |
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# Create a continuous optimization problem |
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X, y = make_regression(n_samples=200, n_features=10, noise=0.1, random_state=42) |
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print( |
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f"Dataset: Synthetic regression ({X.shape[0]} samples, {X.shape[1]} features)" |
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) |
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# Create experiment - neural network with continuous parameters |
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estimator = MLPRegressor(random_state=42, max_iter=1000) |
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experiment = SklearnCvExperiment( |
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estimator=estimator, X=X, y=y, cv=3, scoring="neg_mean_squared_error" |
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) |
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# Define search space - ONLY continuous parameters (CMA-ES limitation) |
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param_space = { |
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"alpha": (1e-6, 1e-1), # L2 regularization |
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"learning_rate_init": (1e-4, 1e-1), # Initial learning rate |
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"beta_1": (0.8, 0.99), # Adam beta1 parameter |
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"beta_2": (0.9, 0.999), # Adam beta2 parameter |
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"epsilon": (1e-9, 1e-6), # Adam epsilon parameter |
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# Note: No categorical parameters - CMA-ES doesn't support them |
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} |
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# Search Space (Continuous parameters only): |
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# for param, space in param_space.items(): |
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# print(f" {param}: {space}") |
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# Note: CMA-ES only works with continuous parameters |
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# For mixed parameter types, consider TPESampler or GPSampler |
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# Configure CmaEsSampler |
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optimizer = CmaEsSampler( |
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param_space=param_space, |
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n_trials=40, |
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random_state=42, |
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experiment=experiment, |
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sigma0=0.2, # Initial step size (exploration vs exploitation) |
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n_startup_trials=5, # Random trials before CMA-ES starts |
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) |
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# CmaEsSampler Configuration: |
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# n_trials: configured above |
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# sigma0: initial step size |
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# n_startup_trials: random trials before CMA-ES starts |
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# Adaptive covariance matrix will be learned during optimization |
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if not cmaes_available: |
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print("⚠ Skipping optimization due to missing 'cmaes' package") |
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print("Install with: pip install cmaes") |
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return None, None |
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# Run optimization |
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# Running CMA-ES optimization... |
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try: |
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best_params = optimizer.run() |
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# Results |
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print("\n=== Results ===") |
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print(f"Best parameters: {best_params}") |
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print(f"Best score: {optimizer.best_score_:.4f}") |
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print() |
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except ImportError as e: |
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print(f"CMA-ES failed: {e}") |
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print("Install the required package: pip install cmaes") |
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return None, None |
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# CMA-ES Behavior Analysis: |
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# Evolution of search distribution: |
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# Initial: Spherical distribution (σ₀ * I) |
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# Early trials: Random exploration to gather information |
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# Mid-trials: Covariance matrix learns parameter correlations |
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# Later trials: Focused search along principal component directions |
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# Adaptive Properties: |
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# Step size (σ) adapts to local topology |
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# Covariance matrix (C) learns parameter interactions |
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# Mean vector (μ) tracks promising regions |
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# Handles ill-conditioned and rotated problems |
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# Best Use Cases: |
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# Continuous optimization problems |
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# Parameters with potential correlations |
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# Non-convex, multimodal functions |
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# When gradient information is unavailable |
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# Medium-dimensional problems (2-40 parameters) |
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# Limitations: |
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# Only continuous parameters (no categorical/discrete) |
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# Requires additional 'cmaes' package |
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# Can be slower than TPE for simple problems |
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# Memory usage grows with parameter dimension |
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if cmaes_available: |
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return best_params, optimizer.best_score_ |
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else: |
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return None, None |
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if __name__ == "__main__": |
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best_params, best_score = main() |
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SimonBlanke /
Hyperactive
