Cumulative Step-size Adaptation on Linear Functions: Technical Report

Alexandre Adrien Chotard; Anne Auger; Nikolaus Hansen

hal-00704903, version 2

Cumulative Step-size Adaptation on Linear Functions: Technical Report

Alexandre Adrien Chotard (, )^a^, 1, 2, Anne Auger (, )^a^, 2, Nikolaus Hansen (, )^a^, 1, 2, 3

(2012)

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.

a – INRIA
1: Laboratoire de Recherche en Informatique (LRI)
CNRS : UMR8623 – Université Paris XI - Paris Sud
2: TAO (INRIA Saclay - Ile de France)
INRIA – CNRS : UMR8623 – Université Paris XI - Paris Sud
3: Microsoft Research - Inria Joint Centre (MSR - INRIA)
INRIA – Microsoft – Microsoft Research Laboratory Cambridge

hal-00704903, version 2
http://hal.inria.fr/hal-00704903
oai:hal.inria.fr:hal-00704903
From: Alexandre Chotard <>
Submitted on: Friday, 29 June 2012 16:30:00
Updated on: Monday, 25 February 2013 16:14:42

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arXiv: 1206.1208

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