Active Covariance Matrix Adaptation

Active covariance matrix adaptation is a mechanism for accelerating the convergence of covariance matrix adaptation evolution strategies (CMA-ES). While "conventional" CMA-ES update their mutation distribution by enlarging variances in successful search directions, active covariance matrix adaptation additionally actively decreases variances in especially unsuccessful directions. This is especially useful for optimisation problems that contain high-dimensional valleys, where the eigenvalue spectrum of the local Hessian is dominated by a small number of relatively large values. We have developed active variants of both (μ/μ,λ)-CMA-ES and (1+1)-CMA-ES.

Publications

G. Jastrebski and D. V. Arnold
Improving evolution strategies through active covariance matrix adaptation
IEEE Congress on Evolutionary Computation, Vancouver, 2006.

D. V. Arnold and N. Hansen
Active covariance matrix adaptation for the (1+1)-CMA-ES
Genetic and Evolutionary Computation Conference, Portland, OR, 2010.

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