Cumulative Step-size Adaptation on Linear Functions

Alexandre Chotard 1, 2 Anne Auger 1 Nikolaus Hansen 1
1 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
Abstract : The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies the CSA-ES on composites of strictly increasing functions with affine linear functions through the investigation of its underlying Markov chains. Rigorous results on the change and the variation of the step size are derived with and without cumulation. The step-size diverges geometrically fast in most cases. Furthermore, the influence of the cumulation parameter is studied.
Type de document :
Communication dans un congrès
PPSN 2012, Sep 2012, Taormina, Italy. Springer, pp.72-81, 2012
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https://hal.inria.fr/hal-00759577
Contributeur : Alexandre Chotard <>
Soumis le : samedi 1 décembre 2012 - 12:17:22
Dernière modification le : jeudi 11 janvier 2018 - 06:22:14
Document(s) archivé(s) le : samedi 17 décembre 2016 - 18:44:00

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  • HAL Id : hal-00759577, version 1
  • ARXIV : 1212.0139

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Alexandre Chotard, Anne Auger, Nikolaus Hansen. Cumulative Step-size Adaptation on Linear Functions. PPSN 2012, Sep 2012, Taormina, Italy. Springer, pp.72-81, 2012. 〈hal-00759577〉

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