Rigorous analysis of some simple adaptive ES

Anne Auger 1, 2 Claude Le Bris 2, 3 Marc Schoenauer 1
1 TANC - Algorithmic number theory for cryptology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
2 MICMAC - Methods and engineering of multiscale computing from atom to continuum
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : Based on the theory of non-negative supermartingales, convergence results are proven for adaptive (1,)-ES with Gaussian mutations, and geometrical convergence rates are derived. In the d-dimensional case (d > 1), the algorithm studied here uses a different step-size update in each direction. However, the critical value for the step-size, and the resulting convergence rate do not depend on the dimension. Those results are discussed with respect to previous works. Thorough numerical investigations on some 1-dimensional functions validate the theoretical results.
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  • HAL Id : inria-00071665, version 1

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Anne Auger, Claude Le Bris, Marc Schoenauer. Rigorous analysis of some simple adaptive ES. [Research Report] RR-4914, INRIA. 2003. ⟨inria-00071665⟩

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