A CMA-ES with multiplicative covariance matrix updates

Oswin Krause; Tobias Glasmachers

doi:10.1145/2739480.2754781

A CMA-ES with multiplicative covariance matrix updates

Oswin Krause, Tobias Glasmachers

Datalogisk Institut

9 Citationer (Scopus)

Abstract

Covariance matrix adaptation (CMA) mechanisms are core building blocks of modern evolution strategies. Despite sharing a common principle, the exact implementation of CMA varies considerably between different algorithms. In this paper, we investigate the benefits of an exponential parametrization of the covariance matrix in the CMA-ES. This technique was first proposed for the xNES algorithm. It results in a multiplicative update formula for the covariance matrix. We show that the exponential parameterization and the multiplicative update are compatible with all mechanisms of CMA-ES. The resulting algorithm, xCMA-ES, performs at least on par with plain CMA-ES. Its advantages show in particular with updates that actively decrease the sampling variance in specific directions, i.e., for active constraint handling.

Originalsprog	Engelsk
Titel	Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation
Antal sider	8
Forlag	Association for Computing Machinery
Publikationsdato	11 jul. 2015
Sider	281-288
ISBN (Trykt)	978-1-4503-3472-3
DOI	https://doi.org/10.1145/2739480.2754781
Status	Udgivet - 11 jul. 2015
Begivenhed	Annual Conference on Genetic and Evolutionary Computation 2015 - Madrid, Spanien Varighed: 11 jul. 2015 → 15 jul. 2015

Konference

Konference	Annual Conference on Genetic and Evolutionary Computation 2015
Land/Område	Spanien
By	Madrid
Periode	11/07/2015 → 15/07/2015

Emneord

cma-es, covariance matrix adaptation, evolution strategies, exponential coordinates, multiplicative update

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10.1145/2739480.2754781

Citationsformater

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title = "A CMA-ES with multiplicative covariance matrix updates",

abstract = "Covariance matrix adaptation (CMA) mechanisms are core building blocks of modern evolution strategies. Despite sharing a common principle, the exact implementation of CMA varies considerably between different algorithms. In this paper, we investigate the benefits of an exponential parametrization of the covariance matrix in the CMA-ES. This technique was first proposed for the xNES algorithm. It results in a multiplicative update formula for the covariance matrix. We show that the exponential parameterization and the multiplicative update are compatible with all mechanisms of CMA-ES. The resulting algorithm, xCMA-ES, performs at least on par with plain CMA-ES. Its advantages show in particular with updates that actively decrease the sampling variance in specific directions, i.e., for active constraint handling.",

keywords = "cma-es, covariance matrix adaptation, evolution strategies, exponential coordinates, multiplicative update",

author = "Oswin Krause and Tobias Glasmachers",

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T1 - A CMA-ES with multiplicative covariance matrix updates

AU - Krause, Oswin

AU - Glasmachers, Tobias

PY - 2015/7/11

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N2 - Covariance matrix adaptation (CMA) mechanisms are core building blocks of modern evolution strategies. Despite sharing a common principle, the exact implementation of CMA varies considerably between different algorithms. In this paper, we investigate the benefits of an exponential parametrization of the covariance matrix in the CMA-ES. This technique was first proposed for the xNES algorithm. It results in a multiplicative update formula for the covariance matrix. We show that the exponential parameterization and the multiplicative update are compatible with all mechanisms of CMA-ES. The resulting algorithm, xCMA-ES, performs at least on par with plain CMA-ES. Its advantages show in particular with updates that actively decrease the sampling variance in specific directions, i.e., for active constraint handling.

AB - Covariance matrix adaptation (CMA) mechanisms are core building blocks of modern evolution strategies. Despite sharing a common principle, the exact implementation of CMA varies considerably between different algorithms. In this paper, we investigate the benefits of an exponential parametrization of the covariance matrix in the CMA-ES. This technique was first proposed for the xNES algorithm. It results in a multiplicative update formula for the covariance matrix. We show that the exponential parameterization and the multiplicative update are compatible with all mechanisms of CMA-ES. The resulting algorithm, xCMA-ES, performs at least on par with plain CMA-ES. Its advantages show in particular with updates that actively decrease the sampling variance in specific directions, i.e., for active constraint handling.

KW - cma-es, covariance matrix adaptation, evolution strategies, exponential coordinates, multiplicative update

U2 - 10.1145/2739480.2754781

DO - 10.1145/2739480.2754781

M3 - Article in proceedings

SN - 978-1-4503-3472-3

SP - 281

EP - 288

BT - Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

PB - Association for Computing Machinery

T2 - Annual Conference on Genetic and Evolutionary Computation 2015

Y2 - 11 July 2015 through 15 July 2015

ER -

A CMA-ES with multiplicative covariance matrix updates

Abstract

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