Cumulative Step-size Adaptation on Linear Functions

Alexandre Chotard 1, 2 Anne Auger 1 Nikolaus Hansen 1
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 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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Conference papers
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https://hal.inria.fr/hal-00759577
Contributor : Alexandre Chotard <>
Submitted on : Saturday, December 1, 2012 - 12:17:22 PM
Last modification on : Sunday, July 21, 2019 - 1:48:04 AM
Long-term archiving on : Saturday, December 17, 2016 - 6:44:00 PM

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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. pp.72-81. ⟨hal-00759577⟩

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