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)

Résumé : 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
Contributeur : Alexandre Chotard <>
Soumis le : Vendredi 29 Juin 2012, 16:30:00
Dernière modification le : Lundi 25 Février 2013, 16:14:42

Voir la fiche détaillée

Documents associés

PDF :

arXiv : 1206.1208

Exporter

Bibtex EndNote TEI RefWorks

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="report"><head>Rapports</head>
<biblStruct type="report" xml:id="hal-00704903"><monogr>
<author><persName><forename>Alexandre</forename><surname>Chotard</surname></persName>
<affiliation>
<orgName type="laboratory">LRI</orgName>
<orgName type="team">Laboratoire de Recherche en Informatique</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR8623</orgName>
<orgName type="institution">Université Paris XI - Paris Sud</orgName>
</affiliation>
<affiliation>
<orgName type="laboratory">INRIA Saclay - Ile de France</orgName>
<orgName type="team">TAO</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">CNRS : UMR8623</orgName>
<orgName type="institution">Université Paris XI - Paris Sud</orgName>
</affiliation>
</author>
<author><persName><forename>Anne</forename><surname>Auger</surname></persName>
<affiliation>
<orgName type="laboratory">INRIA Saclay - Ile de France</orgName>
<orgName type="team">TAO</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">CNRS : UMR8623</orgName>
<orgName type="institution">Université Paris XI - Paris Sud</orgName>
</affiliation>
</author>
<author><persName><forename>Nikolaus</forename><surname>Hansen</surname></persName>
<affiliation>
<orgName type="laboratory">LRI</orgName>
<orgName type="team">Laboratoire de Recherche en Informatique</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR8623</orgName>
<orgName type="institution">Université Paris XI - Paris Sud</orgName>
</affiliation>
<affiliation>
<orgName type="laboratory">INRIA Saclay - Ile de France</orgName>
<orgName type="team">TAO</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">CNRS : UMR8623</orgName>
<orgName type="institution">Université Paris XI - Paris Sud</orgName>
</affiliation>
<affiliation>
<orgName type="laboratory">MSR - INRIA</orgName>
<orgName type="team">Microsoft Research - Inria Joint Centre</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">Microsoft</orgName>
<orgName type="institution">Microsoft Research Laboratory Cambridge</orgName>
</affiliation>
</author>
<title type="main" level="m">Cumulative Step-size Adaptation on Linear Functions: Technical Report</title><title type="main" level="m">Cumulative Step-size Adaptation on Linear Functions: Technical Report</title><imprint><biblScope type="publicationDate">2012-06-06</biblScope><biblScope type="pp">23</biblScope></imprint></monogr><idno type="HALid">http://hal.inria.fr/hal-00704903</idno><idno type="HALFile">http://hal.inria.fr/hal-00704903/PDF/cumulationonlinearfunctionppsn_technicalreport.pdf</idno></biblStruct>
</listBibl>
</listBibl>