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

Department of Computer Science

9 Citations (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.

Original language	English
Title of host publication	Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation
Number of pages	8
Publisher	Association for Computing Machinery
Publication date	11 Jul 2015
Pages	281-288
ISBN (Print)	978-1-4503-3472-3
DOIs	https://doi.org/10.1145/2739480.2754781
Publication status	Published - 11 Jul 2015
Event	Annual Conference on Genetic and Evolutionary Computation 2015 - Madrid, Spain Duration: 11 Jul 2015 → 15 Jul 2015

Conference

Conference	Annual Conference on Genetic and Evolutionary Computation 2015
Country/Territory	Spain
City	Madrid
Period	11/07/2015 → 15/07/2015

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10.1145/2739480.2754781

Cite this

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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.",

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T1 - A CMA-ES with multiplicative covariance matrix updates

AU - Krause, Oswin

AU - Glasmachers, Tobias

PY - 2015/7/11

Y1 - 2015/7/11

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

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