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inria-00173483, version 3

Log-linear Convergence and Optimal Bounds for the $(1+1)$-ES

Mohamed Jebalia () a, 1, Anne Auger () a, 1, Pierre Liardet () 2

Evolution Artificielle (2007)

Résumé : The $(1+1)$-ES is modeled by a general stochastic process whose asymptotic behavior is investigated. Under general assumptions, it is shown that the convergence of the related algorithm is sub-log-linear, bounded below by an explicit log-linear rate. For the specific case of spherical functions and scale-invariant algorithm, it is proved using the Law of Large Numbers for orthogonal variables, that the linear convergence holds almost surely and that the best convergence rate is reached. Experimental simulations illustrate the theoretical results.

  • a –  INRIA
  • 1 :  TAO (INRIA Futurs)
  • INRIA – CNRS : UMR8623 – Université Paris XI - Paris Sud
  • 2 :  Centre de Mathématiques et Informatique (CMI)
  • Université de Provence - Aix-Marseille I
 
  • inria-00173483, version 3
  • http://hal.inria.fr/inria-00173483
  • oai:hal.inria.fr:inria-00173483
  • Contributeur : Anne Auger <>
  • Soumis le : Jeudi 3 Juillet 2008, 12:00:26
  • Dernière modification le : Jeudi 3 Juillet 2008, 12:03:13