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BCMA-ES II: revisiting Bayesian CMA-ES

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 cc
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.
Mots-clés
CMA ES; Bayesian; conjugate prior; normal Wishart; normal inverse Wishart; mixture models