BCMA-ES II: revisiting Bayesian CMA-ES

Benhamou, Éric; Saltiel, David; Guez, Beatrice; Paris, Nicolas

Benhamou, Éric; Saltiel, David; Guez, Beatrice; Paris, Nicolas (2020), BCMA-ES II: revisiting Bayesian CMA-ES. https://basepub.dauphine.fr/handle/123456789/21207

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Type

Document de travail / Working paper

Lien vers un document non conservé dans cette base

https://hal.archives-ouvertes.fr/hal-02886508

Date

2020

Titre de la collection

Preprint Lamsade

Ville d’édition

Paris

Métadonnées

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Auteur(s)

Benhamou, Éric
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Saltiel, David
Guez, Beatrice
Paris, Nicolas

Centre de Recherche en Informatique de Lens [CRIL]

Résumé (EN)

This paper revisits the Bayesian CMA-ES and provides updates for normal Wishart. It emphasizes the difference between a normal and normal inverse Wishart prior. After some computation, we prove that the only difference relies surprisingly in the expected covariance. We prove that the expected covariance should be lower in the normal Wishart prior model because of the convexity of the inverse. We present a mixture model that generalizes both normal Wishart and normal inverse Wishart model. We finally present various numerical experiments to compare both methods as well as the generalized method.