# BCMA-ES: A Bayesian approach to CMA-ES

## TL;DR

This paper presents a Bayesian framework for CMA-ES, deriving optimal parameter updates using conjugate priors, leading to two new variants with demonstrated fast convergence in experiments.

## Contribution

It introduces a theoretically grounded Bayesian approach to CMA-ES, resulting in two novel algorithm versions based on different prior assumptions.

## Key findings

- Fast convergence of the proposed CMA-ES variants
- Theoretical justification for CMA-ES updates
- Introduction of normal-Wishart and normal-Inverse Wishart based CMA-ES variants

## Abstract

This paper introduces a novel theoretically sound approach for the celebrated CMA-ES algorithm. Assuming the parameters of the multi variate normal distribution for the minimum follow a conjugate prior distribution, we derive their optimal update at each iteration step. Not only provides this Bayesian framework a justification for the update of the CMA-ES algorithm but it also gives two new versions of CMA-ES either assuming normal-Wishart or normal-Inverse Wishart priors, depending whether we parametrize the likelihood by its covariance or precision matrix. We support our theoretical findings by numerical experiments that show fast convergence of these modified versions of CMA-ES.