Evolution under strong noise: A self-adaptive evolution strategy can reach the lower performance bound - the pcCMSA-ES

Abstract

According to a theorem by Astete-Morales, Cauwet, and Teytaud, “simple Evolution Strategies (ES)” that optimize quadratic functions disturbed by additive Gaussian noise of constant variance can only reach a simple regret log-log convergence slope ≥ −1/2 (lower bound). In this paper a population size controlled ES is presented that is able to perform better than the −1/2 limit. It is shown experimentally that the pcCMSA-ES is able to reach a slope of −1 being the theoretical lower bound of all comparison-based direct search algorithms.