A Simple Modification in CMA-ES Achieving Linear Time and Space Complexity

This report proposes a simple modification of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for high dimensional objective functions, that reduces the internal time and space complexity from quadratic to linear. The covariance matrix is constrained to be diagonal and the resulting algorithm, sep-CMA-ES, samples each coordinate independently. Because the model complexity is reduced, the learning rate for the covariance matrix can be increased. Consequently, on essentially separable functions, sep-CMA-ES significantly outperforms CMA-ES. For dimensions larger than 100, even on the non-separable Rosenbrock function, the sep-CMA-ES needs fewer function evaluations than CMA-ES. Key-words: Evolution Strategy, Performance Assessment, Separability, Covariance Matrix Adaptation, Time Complexity in ria -0 02 70 90 1, v er si on 4 30 J un 2 00 8 Une Simple Modification dans CMA-ES pour une Complexité Spatiale et Temporelle Linéaire Résumé : Pas de résumé Mots-clés : Pas de motclef in ria -0 02 70 90 1, v er si on 4 30 J un 2 00 8 A simple modification in CMA-ES achieving linear complexity. 3