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Cumulative Step-size Adaptation on Linear Functions: Technical Report

Alexandre Chotard 1 Anne Auger 1 Nikolaus Hansen 2, 1, 3
1 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 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 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.
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Contributor : Alexandre Chotard <>
Submitted on : Friday, June 29, 2012 - 4:30:00 PM
Last modification on : Monday, December 9, 2019 - 5:24:06 PM
Document(s) archivé(s) le : Thursday, December 15, 2016 - 4:26:41 PM


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  • HAL Id : hal-00704903, version 2
  • ARXIV : 1206.1208



Alexandre Chotard, Anne Auger, Nikolaus Hansen. Cumulative Step-size Adaptation on Linear Functions: Technical Report. [Research Report] 2012, pp.23. ⟨hal-00704903v2⟩



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