Population Size Adaptation for the CMA-ES Based on the Estimation Accuracy of the Natural Gradient

Abstract

We propose a novel strategy to adapt the population size, i.e. the number of candidate solutions per iteration, for the rank-mu update covariance matrix adaptation evolution strategy (CMA-ES). Our strategy is based on the interpretation of the rank-mu update CMA-ES as the stochastic natural gradient approach on the parameter space of the sampling distribution. We introduce a measurement of the accuracy of the current estimate of the natural gradient. We propose a novel strategy to adapt the population size according to the accuracy measure. The proposed strategy is evaluated on test functions including rugged functions and noisy functions where a larger population size is known to help to find a better solution. The experimental results show the advantage of the adaptation of the population size over a fixed population size. It is also compared with the state-of-the-art uncertainty handling strategy for the CMA-ES, namely UH-CMA-ES, on noisy test functions.