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Conference papers

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.
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Contributor : Alexandre Chotard <>
Submitted on : Saturday, December 1, 2012 - 12:17:22 PM
Last modification on : Tuesday, June 15, 2021 - 4:07:10 PM
Long-term archiving on: : Saturday, December 17, 2016 - 6:44:00 PM


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



Alexandre Chotard, Anne Auger, Nikolaus Hansen. Cumulative Step-size Adaptation on Linear Functions. PPSN 2012 - 12th International Conference on Parallel Problem Solving From Nature, Sep 2012, Taormina, Italy. pp.72-81. ⟨hal-00759577⟩



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