Decoupling of Direction and Length for Cumulative Step Size Adaptation

Covariance matrix adaptation evolution strategy (CMA-ES) is a successful evolutionary algorithm for continuous optimization. The cumulative step size adaptation (CSA) is the default method for adapting the step size in CMA-ES and achieves remarkable performance in practice. It follows the idea of exploiting the correlations between search directions in consecutive generations. In this paper, we investigate the effects of the update directions and the length in CSA. We find that sampling from uniform sphere distribution can yield comparative performance to the default setting, and normalizing the update direction in CSA does not hurt the performance. Further, the CSA with actual search direction cannot perform well, and the correlation between the default direction of CSA and the actual search direction is rather small. It indicates that CSA does not accumulate the actual search directions. We argue that the step size and the covariance matrix should be updated by decoupled search information, and accumulating the actual search direction results in inferior performance due to the same update direction in two evolution paths for the step size and covariance matrix updates.