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

Abstract
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. This paper shows that the underlying basic assumption in CSA — the perpendicularity of expected consecutive steps — does not necessarily guarantee optimal progress performance for (μ/μIλ) intermediate recombinative ES