  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.
