Mirrored Sampling and Sequential Selection for Evolution Strategies

Dimo Brockhoff (1) , Anne Auger (1) , Nikolaus Hansen (1) , Dirk V. Arnold (2) , Tim Hohm (3)

1 TAO - Machine Learning and Optimisation
2 Faculty of Computer Science
3 ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]

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 about 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 it- eration 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, λ)-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 the (1,4)-ES becomes about 10% faster than the (1+1)-ES. 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.

Domains: Machine Learning [cs.LG]

Dimo Brockhoff, Anne Auger, Nikolaus Hansen, Dirk V. Arnold, Tim Hohm. Mirrored Sampling and Sequential Selection for Evolution Strategies. PPSN, Sep 2010, Warsaw, Poland. pp.11-21. ⟨inria-00530202v2⟩