BCMA-ES: A Bayesian approach to CMA-ES

Benhamou, Éric; Saltiel, David; Verel, Sébastien; Teytaud, Fabien

Benhamou, Éric; Saltiel, David; Verel, Sébastien; Teytaud, Fabien (2020), BCMA-ES: A Bayesian approach to CMA-ES. https://basepub.dauphine.fr/handle/123456789/21201

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Type

Document de travail / Working paper

External document link

https://hal.archives-ouvertes.fr/hal-02886512

Date

2020

Series title

Preprint Lamsade

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Author(s)

Benhamou, Éric
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Saltiel, David
Verel, Sébastien

Teytaud, Fabien

Abstract (EN)

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.

Subjects / Keywords

CMA-ES; Bayesian; conjugate prior; normal-inverse-Wishart