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

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 (mu/mu(I), lambda) intermediate recombinative ES.