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

Raymond Ros 1 Nikolaus Hansen 1, 2 
1 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : This paper proposes a simple modification of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for high dimensional objective functions, reducing 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 a hundred, even on the non-separable Rosenbrock function, the sep-CMA-ES needs fewer function evaluations than CMA-ES.
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Submitted on : Monday, June 23, 2008 - 6:04:18 PM
Last modification on : Friday, November 18, 2022 - 9:23:32 AM
Long-term archiving on: : Friday, September 28, 2012 - 3:51:01 PM


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  • HAL Id : inria-00287367, version 1


Raymond Ros, Nikolaus Hansen. A Simple Modification in CMA-ES Achieving Linear Time and Space Complexity. 10th International Conference on Parallel Problem Solving From Nature, Sep 2008, Dortmund, Germany. ⟨inria-00287367⟩



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