Abnormal Mutations: Evolution Strategies Don't Require Gaussianity

TL;DR

This paper demonstrates that evolution strategies can effectively use non-Gaussian mutation distributions, such as uniform, without performance loss across various benchmark problems, challenging the traditional reliance on Gaussian mutations.

Contribution

It empirically shows that evolution strategies are robust to the choice of mutation distribution, extending beyond the standard Gaussian to other distributions like uniform.

Findings

Non-Gaussian mutations perform comparably to Gaussian in ES.

Performance remains stable across different benchmark problems.

Results challenge the necessity of Gaussianity in mutation distributions.

Abstract

The mutation process in evolution strategies has been interlinked with the normal distribution since its inception. Many lines of reasoning have been given for this strong dependency, ranging from maximum entropy arguments to the need for isotropy. However, some theoretical results suggest that other distributions might lead to similar local convergence properties. This paper empirically shows that a wide range of evolutionary strategies, from the (1+1)-ES to CMA-ES, show comparable optimization performance when using a mutation distribution other than the standard Gaussian. Replacing it with, e.g., uniformly distributed mutations, does not deteriorate the performance of ES, when using the default adaptation mechanism for the strategy parameters. We observe that these results hold not only for the sphere model but also for a wider range of benchmark problems.