BCMA-ES: A Bayesian approach to CMA-ES
This work provides a theoretically sound justification for CMA-ES updates, which is incremental but addresses a known bottleneck in evolutionary computation for optimization practitioners.
The paper tackles the problem of improving the theoretical foundation and performance of the CMA-ES algorithm by introducing a Bayesian framework, resulting in two new versions that show fast convergence in numerical experiments.
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.