BCMA-ES II: Revisiting Bayesian 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; AI For Alpha; EB AI Advisory; Université Paris-Dauphine, PSL Research University

David Saltiel

Université Paris Dauphine; A.I. Square Connect; AI For Alpha

Beatrice Guez

AI For Alpha

Nicolas Paris

A.I. Square Connect

Date Written: March 3, 2019

Abstract

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.

Keywords: CMA ES, Bayesian, conjugate prior, normal Wishart, normal inverse Wishart, mixture models

JEL Classification: C61, C11

Suggested Citation

Benhamou, Eric and Saltiel, David and Guez, Beatrice and Paris, Nicolas, BCMA-ES II: Revisiting Bayesian CMA-ES (March 3, 2019). A.I Square Working Paper, March 2019, France, Available at SSRN: https://ssrn.com/abstract=3365453 or http://dx.doi.org/10.2139/ssrn.3365453

Eric Benhamou

Université Paris Dauphine ( email )

Place du Maréchal de Tassigny
Paris, Cedex 16 75775
France

AI For Alpha ( email )

35 boulevard d'Inkermann
Neuilly sur Seine, 92200
France

EB AI Advisory ( email )

35 Boulevard d'Inkermann
Neuilly sur Seine, 92200
France

Université Paris-Dauphine, PSL Research University ( email )

Place du Maréchal de Lattre de Tassigny
Paris, 75016
France

David Saltiel (Contact Author)

Université Paris Dauphine ( email )

Place du Maréchal de Tassigny
Paris, Cedex 16 75775
France

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

Beatrice Guez

AI For Alpha ( email )

35 boulevard d'Inkermann
Neuilly sur Seine, 92200
France

Nicolas Paris

A.I. Square Connect ( email )

35 Boulevard d'Inkermann
Neuilly sur Seine, 92200
France

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