Maximum Likelihood-based Online Adaptation of Hyper-parameters in CMA-ES

TL;DR

This paper introduces self-CMA-ES, a method for online hyper-parameter adaptation in CMA-ES, improving its performance especially with larger population sizes by dynamically tuning parameters.

Contribution

The paper presents a novel online hyper-parameter adaptation method for CMA-ES, enhancing its robustness and efficiency in non-linear optimization tasks.

Findings

Self-CMA-ES improves performance with larger population sizes.

Default hyper-parameters are suboptimal for larger populations.

Dynamic tuning approaches optimal hyper-parameter settings.

Abstract

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is widely accepted as a robust derivative-free continuous optimization algorithm for non-linear and non-convex optimization problems. CMA-ES is well known to be almost parameterless, meaning that only one hyper-parameter, the population size, is proposed to be tuned by the user. In this paper, we propose a principled approach called self-CMA-ES to achieve the online adaptation of CMA-ES hyper-parameters in order to improve its overall performance. Experimental results show that for larger-than-default population size, the default settings of hyper-parameters of CMA-ES are far from being optimal, and that self-CMA-ES allows for dynamically approaching optimal settings.