HAL - INRIA :: [hal-00217562, version 1] Convergence properties of the expected improvement algorithm with fixed mean and covariance functions

hal-00217562, version 1

Convergence properties of the expected improvement algorithm with fixed mean and covariance functions

Emmanuel Vazquez () ^1, 2, Julien Bect (, ) ^1, 2

Journal of Statistical Planning and Inference 140, 11 (2010) 3088-3095

Abstract: This paper deals with the convergence of the expected improvement algorithm, a popular global optimization algorithm based on a Gaussian process model of the function to be optimized. The first result is that under some mild hypotheses on the covariance function k of the Gaussian process, the expected improvement algorithm produces a dense sequence of evaluation points in the search domain, when the function to be optimized is in the reproducing kernel Hilbert space generated by k. The second result states that the density property also holds for P-almost all continuous functions, where P is the (prior) probability distribution induced by the Gaussian process.

1: Supélec Sciences des Systèmes - EA4454 (E3S)
SUPELEC
2: GdR MASCOT-NUM ((Méthodes d'Analyse Stochastique des Codes et Traitements Numériques))
CNRS : GDR3179

hal-00217562, version 1
http://hal-supelec.archives-ouvertes.fr/hal-00217562
oai:hal-supelec.archives-ouvertes.fr:hal-00217562
From: Julien Bect <>
Submitted on: Wednesday, 19 May 2010 21:18:34
Updated on: Thursday, 2 December 2010 11:16:38

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DOI: 10.1016/j.jspi.2010.04.018

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