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1 LRI - Laboratoire de Recherche en Informatique 2 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 : The mathematical analysis of optimization algorithms involves upper and lower bounds; we here focus on the second case. Whereas other chap- ters will consider black box complexity, we will here consider complexity based on the key assumption that the only information available on the fitness values is the rank of individuals - we will not make use of the exact fitness values. Such a reduced information is known efficient in terms of ro- bustness Gelly et al., 2007, what gives a solid theoretical foundation to the robustness of evolution strategies, which is often argued without mathemat- ical rigor - and we here show the implications of this reduced information on convergence rates. In particular, our bounds are proved without infi- nite dimension assumption, and they have been used since that time for designing algorithms with better performance in the parallel setting.

Author: Olivier Teytaud -

Source: https://hal.archives-ouvertes.fr/


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