BCMA-ES: A Bayesian Approach to CMA-ES

A.I Square Working Paper, March 2019, France

10 Pages Posted: 6 May 2019

See all articles by Eric Benhamou

Eric Benhamou

Université Paris Dauphine; EB AI Advisory; AI For Alpha

David Saltiel

A.I. Square Connect; AI For Alpha

Sebastien Verel

affiliation not provided to SSRN

Fabien Teytaud

affiliation not provided to SSRN

Date Written: March 3, 2019

Abstract

This paper introduces a novel theoretically sound approach for the celebrated CMA-ES algorithm. Assuming the parameters of the multi variate normal distribution for the minimum follow a conjugate prior distribution, we derive their optimal update at each iteration step. Not only provides this Bayesian framework a justification for the update of the CMA-ES algorithm but it also gives two new versions of CMA-ES either assuming normal-Wishart or normal-Inverse Wishart priors, depending whether we parametrize the likelihood by its covariance or precision matrix. We support our theoretical findings by numerical experiments that show fast convergence of these modified versions of CMA-ES.

Keywords: CMA-ES, Bayesian, Conjugate Prior, Normal-Inverse-Wishart

JEL Classification: C61, C11

Suggested Citation

Benhamou, Eric and Saltiel, David and Verel, Sebastien and Teytaud, Fabien, BCMA-ES: A Bayesian Approach to CMA-ES (March 3, 2019). A.I Square Working Paper, March 2019, France, Available at SSRN: https://ssrn.com/abstract=3365449 or http://dx.doi.org/10.2139/ssrn.3365449

Eric Benhamou

Université Paris Dauphine ( email )

Place du Maréchal de Tassigny
Paris, Cedex 16 75775
France

EB AI Advisory ( email )

35 Boulevard d'Inkermann
Neuilly sur Seine, 92200
France

AI For Alpha ( email )

35 boulevard d'Inkermann
Neuilly sur Seine, 92200
France

David Saltiel (Contact Author)

A.I. Square Connect ( email )

35 Boulevard d'Inkermann
Neuilly sur Seine, 92200
France

AI For Alpha ( email )

35 boulevard d'Inkermann
Neuilly sur Seine, 92200
France

Sebastien Verel

affiliation not provided to SSRN

Fabien Teytaud

affiliation not provided to SSRN

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