BCMA-ES II: Revisiting Bayesian CMA-ES

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