Active Update of Mutation Matrix Adaptation for Variable Metric Evolution Strategy

Covariance matrix adaptation evolution strategy (CMA-ES) is one of the most successful evolutionary algorithms. To improve the efficiency of CMA-ES and make sufficient use of the sampled points, we propose an active update scheme for the mutation matrix which approximates the factorization of the covariance matrix. The active update effectively reduces the variance along undesired search directions with negative weights. We design a set of symmetric weights for all the sampled points as well as a larger learning rate. We conduct extensive experiments and show that the proposed active update scheme effectively accelerates the convergence to the optimum.