Mirrored Sampling and Sequential Selection for Evolution Strategies

Anne Auger 1 Dimo Brockhoff 1 Nikolaus Hansen 1
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 reveals the surprising result that a single-parent non-elitist evolution strategy (ES) can be locally faster than the (1+1)-ES. The result is brought by mirrored sampling and sequential selection. With mirrored sampling, two offspring are generated symmetrically or mirrored with respect to their parent. In sequential selection, the offspring are evaluated sequentially and the iteration is concluded as soon as one offspring is better than the current parent. Both concepts complement each other well. We derive exact convergence rates of the $(1,\lambda)$-ES with mirrored sampling and/or sequential selection on the sphere model. The log-linear convergence of the ES is preserved. Both methods lead to an improvement and in combination they can sometimes even double the convergence rate. Naively implemented into the CMA-ES with recombination, mirrored sampling leads to a bias on the step-size. However, the (1,4)-CMA-ES with mirrored sampling and sequential selection is unbiased and appears to be faster, more robust, and as local as the (1+1)-CMA-ES.
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[Research Report] RR-7249, INRIA. 2010
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Anne Auger, Dimo Brockhoff, Nikolaus Hansen. Mirrored Sampling and Sequential Selection for Evolution Strategies. [Research Report] RR-7249, INRIA. 2010. 〈inria-00472650v2〉

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