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

Raymond Ros 1, 2 Nikolaus Hansen 1
1 TANC - Algorithmic number theory for cryptology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7161
Abstract : 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 dimension larger than 100, even on the non-separable Rosenbrock function, the sep-CMA-ES needs fewer function evaluations than CMA-ES.
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[Research Report] RR-6498, INRIA. 2008
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Raymond Ros, Nikolaus Hansen. A Simple Modification in CMA-ES Achieving Linear Time and Space Complexity. [Research Report] RR-6498, INRIA. 2008. 〈inria-00270901v4〉

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