
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 paperExternal document link
https://hal.archives-ouvertes.fr/hal-02886508Date
2020Series title
Preprint LamsadePublished in
Paris
Metadata
Show full item recordAuthor(s)
Benhamou, ÉricLaboratoire 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]
Abstract (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.Subjects / Keywords
CMA ES; Bayesian; conjugate prior; normal Wishart; normal inverse Wishart; mixture modelsRelated items
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