A CMA-ES with Multiplicative Covariance Matrix Updates
Oswin Krause, Tobias Glasmachers · 2015
Covariance matrix adaptation (CMA) mechanisms are core building blocks of modern evolution strategies. Despite sharing a common principle, the exact implementation of CMA varies considerably between different algorithms. In this paper, we investigate the benefits of an exponential parametrization of the covariance matrix in the CMA-ES. This technique was first proposed for the xNES algorithm. It results in a multiplicative update formula for the covariance matrix. We show that the exponential parameterization and the multiplicative update are compatible with all mechanisms of CMA-ES. The resulting algorithm, xCMA-ES, performs at least on par with plain CMA-ES. Its advantages show in particular with updates that actively decrease the sampling variance in specific directions, i.e., for active constraint handling.