CMA-ES

Lightweight Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [1] implementation.

Himmelblau function.

Rosenbrock function.

Quadratic function.

These GIF animations are generated by visualizer.py.

Installation

Supported Python versions are 3.5 or later.

$ pip install cmaes

Or you can install via conda-forge.

$ conda install -c conda-forge cmaes

Usage

This library provides two interfaces that an Optuna's sampler interface and a low-level interface. I recommend you to use this library via Optuna.

Optuna's sampler interface

Optuna [2] is an automatic hyperparameter optimization framework. A sampler based on this library is available from Optuna v1.3.0. Usage is like this:

import optuna

def objective(trial: optuna.Trial):
    x1 = trial.suggest_uniform("x1", -4, 4)
    x2 = trial.suggest_uniform("x2", -4, 4)
    return (x1 - 3) ** 2 + (10 * (x2 + 2)) ** 2

if __name__ == "__main__":
    sampler = optuna.samplers.CmaEsSampler()
    study = optuna.create_study(sampler=sampler)
    study.optimize(objective, n_trials=250)

See the documentation for more details.

Monkeypatch for faster CMA-ES sampler of Optuna v1.3.x.

If you are using Optuna v1.3.x, you can make optuna.samplers.CmaEsSampler faster.

import optuna
from cmaes.monkeypatch import patch_fast_intersection_search_space

patch_fast_intersection_search_space()

def objective(trial: optuna.Trial):
    x1 = trial.suggest_float("x1", -4, 4)
    x2 = trial.suggest_float("x2", -4, 4)
    return (x1 - 3) ** 2 + (10 * (x2 + 2)) ** 2

if __name__ == "__main__":
    sampler = optuna.samplers.CmaEsSampler()
    study = optuna.create_study(sampler=sampler)
    study.optimize(objective, n_trials=250)

For older versions (Optuna v1.2.0 or older)

If you are using older versions, please use cmaes.samlper.CMASampler.

import optuna
from cmaes.sampler import CMASampler

def objective(trial: optuna.Trial):
    x1 = trial.suggest_uniform("x1", -4, 4)
    x2 = trial.suggest_uniform("x2", -4, 4)
    return (x1 - 3) ** 2 + (10 * (x2 + 2)) ** 2

if __name__ == "__main__":
    sampler = CMASampler()
    study = optuna.create_study(sampler=sampler)
    study.optimize(objective, n_trials=250)

Note that CmaEsSampler doesn't support categorical distributions. If your search space contains a categorical distribution, please use TPESampler.

Low-level interface

This library also provides an "ask-and-tell" style interface.

import numpy as np
from cmaes import CMA

def quadratic(x1, x2):
    return (x1 - 3) ** 2 + (10 * (x2 + 2)) ** 2

if __name__ == "__main__":
    cma_es = CMA(mean=np.zeros(2), sigma=1.3)

    for generation in range(50):
        solutions = []
        for _ in range(cma_es.population_size):
            x = cma_es.ask()
            value = quadratic(x[0], x[1])
            solutions.append((x, value))
            print(f"#{generation} {value} (x1={x[0]}, x2 = {x[1]})")
        cma_es.tell(solutions)

Benchmark results

Rosenbrock function	Six-Hump Camel function

This implementation (green) stands comparison with pycma (blue). See benchmark for details.

Links

Other libraries:

I respect all libraries involved in CMA-ES.

• pycma : Most famous CMA-ES implementation by Nikolaus Hansen.
• libcmaes: Multithreaded C++11 library with Python bindings.
• cma-es : A Tensorflow v2 implementation.

References:

• [1] N. Hansen, The CMA Evolution Strategy: A Tutorial. arXiv:1604.00772, 2016.
• [2] Takuya Akiba, Shotaro Sano, Toshihiko Yanase, Takeru Ohta, Masanori Koyama. 2019. Optuna: A Next-generation Hyperparameter Optimization Framework. In The 25th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD ’19), August 4–8, 2019.