Dimension-independent convergence rate for non-isotropic (1, λ) - ES

Anne Auger; Claude Le Bris; Marc Schoenauer

doi:10.1007/3-540-45105-6_64

Dimension-independent convergence rate for non-isotropic (1, λ) - ES

Anne Auger, Claude Le Bris, Marc Schoenauer

Research output: Contribution to journal › Article › peer-review

Abstract

Based on the theory of non-negative super martingales, convergence results are proven for adaptive (1,λ) - ES (i.e. with Gaussian mutations), and geometrical convergence rates are derived. In the d-dimensional case (d > 1), the algorithm studied here uses a different step-size update in each direction. However, the critical value for the step-size, and the resulting convergence rate do not depend on the dimension. Those results are discussed with respect to previous works. Rigorous numerical investigations on some 1-dimensional functions validate the theoretical results. Trends for future research are indicated.

Original language	English
Pages (from-to)	512-524
Number of pages	13
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2723
DOIs	https://doi.org/10.1007/3-540-45105-6_64
Publication status	Published - 1 Jan 2003
Externally published	Yes

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title = "Dimension-independent convergence rate for non-isotropic (1, λ) - ES",

abstract = "Based on the theory of non-negative super martingales, convergence results are proven for adaptive (1,λ) - ES (i.e. with Gaussian mutations), and geometrical convergence rates are derived. In the d-dimensional case (d > 1), the algorithm studied here uses a different step-size update in each direction. However, the critical value for the step-size, and the resulting convergence rate do not depend on the dimension. Those results are discussed with respect to previous works. Rigorous numerical investigations on some 1-dimensional functions validate the theoretical results. Trends for future research are indicated.",

author = "Anne Auger and \{Le Bris\}, Claude and Marc Schoenauer",

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AU - Auger, Anne

AU - Le Bris, Claude

AU - Schoenauer, Marc

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N2 - Based on the theory of non-negative super martingales, convergence results are proven for adaptive (1,λ) - ES (i.e. with Gaussian mutations), and geometrical convergence rates are derived. In the d-dimensional case (d > 1), the algorithm studied here uses a different step-size update in each direction. However, the critical value for the step-size, and the resulting convergence rate do not depend on the dimension. Those results are discussed with respect to previous works. Rigorous numerical investigations on some 1-dimensional functions validate the theoretical results. Trends for future research are indicated.

AB - Based on the theory of non-negative super martingales, convergence results are proven for adaptive (1,λ) - ES (i.e. with Gaussian mutations), and geometrical convergence rates are derived. In the d-dimensional case (d > 1), the algorithm studied here uses a different step-size update in each direction. However, the critical value for the step-size, and the resulting convergence rate do not depend on the dimension. Those results are discussed with respect to previous works. Rigorous numerical investigations on some 1-dimensional functions validate the theoretical results. Trends for future research are indicated.

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JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -

Dimension-independent convergence rate for non-isotropic (1, λ) - ES

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