cmaes 0.3.1

Lightweight Covariance Matrix Adaptation Evolution Strategy (CMA-ES) implementation for Python 3.

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 3.6 or later.

$ pip install 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. Optuna officially implements a sampler based on pycma. It achieves almost the same performance. But this library is faster and simple.

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 CMASampler doesn't support categorical distributions. Although pycma's sampler supports categorical distributions, it also has a problem (especially on high-cardinality categorical distribution). If your search space contains a categorical distribution, please use TPESampler.

Low-level 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

Algorithm's efficiency

Rosenbrock function	Six-Hemp Camel function

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

Execution Speed

trials/params	storage	pycma's sampler	this library
100 / 5	memory	4.976 sec (+/- 0.596)	0.197 sec (+/- 0.078)
500 / 5	memory	71.651 sec (+/- 3.847)	0.656 sec (+/- 0.044)
500 / 50	memory	291.002 sec (+/- 5.010)	1.981 sec (+/- 0.041)
100 / 5	sqlite	16.143 sec (+/- 3.487)	11.843 sec (+/- 1.390)
500 / 5	sqlite	129.436 sec (+/- 6.279)	43.735 sec (+/- 2.676)
500 / 50	sqlite	397.084 sec (+/- 6.618)	150.531 sec (+/- 1.113)

This script was run on my laptop with --times 4. So the times should not be taken precisely. Even though, it is clear that this library is extremely faster than Optuna's pycma sampler (with Optuna v1.0.0 and pycma v2.7.0).

Links

Other libraries:

I respect all libraries involved in CMA-ES.

• pycma : Most famous CMA-ES implementation by Nikolaus Hansen.
• 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.