Qualms Regarding the Optimality of Cumulative Path Length Control in CSA/CMA-Evolution Strategies

Abstract

The cumulative step-size adaptation (CSA) based on path length control is regarded as a robust alternative to the standard mutative self-adaptation technique in evolution strategies (ES), guaranteeing an almost optimal control of the mutation operator. In this short paper it is shown that the underlying basic assumption in CSA - the perpendicularity of expected consecutive steps - does not necessarily guarantee optimal progress performance for (...)intermediate recombinative ES.