BCMA-ES II: revisiting Bayesian CMA-ES
This work provides incremental improvements to Bayesian CMA-ES, a method for optimization in evolutionary algorithms, by clarifying prior effects and proposing a generalization.
The paper revisits Bayesian CMA-ES, analyzing differences between normal Wishart and normal inverse Wishart priors, proving that the expected covariance is lower in the normal Wishart model due to convexity, and introduces a mixture model generalizing both, with numerical experiments comparing the methods.
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.