Abstract
Regarding the noisy ellipsoid model with additive Gaussian noise, the population control covariance matrix self-adaptation Evolution Strategy (pcCMSA-ES) by Hellwig and Beyer was empirically observed to exhibit a convergence rate (CR) close to the theoretical lower bound of - 1 for all comparison-based direct search algorithms. The present paper provides the corresponding theoretical analysis of the pcCMSA-ES long-term behavior. To this end, the analysis from the context of isotropic mutations is transferred to the pcCMSA-ES that uses covariance matrix adaptation until significant noise influence is detected. The results allow for the computation of an upper bound on the number of generations between two consecutive test decisions of the pcCMSA-ES that ensures the observed performance. Further, the empirically observed convergence rate of CR ∼ −1 is theoretically derived.
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