  In this paper we propose a technique to reduce the number of function
evaluations, which is often the bottleneck of the black-box optimization, in
the information geometric optimization (IGO) that is a generic framework of the
probability model-based black-box optimization algorithms and generalizes
several well-known evolutionary algorithms, such as the population-based
incremental learning (PBIL) and the pure rank-$\mu$ update covariance matrix
adaptation evolution strategy (CMA-ES). In each iteration, the IGO algorithms
update the parameters of the probability distribution to the natural gradient
direction estimated by Monte-Carlo with the samples drawn from the current
distribution. Our strategy is to reuse previously generated and evaluated
samples based on the importance sampling. It is a technique to reduce the
estimation variance without introducing a bias in Monte-Carlo estimation. We
apply the sample reuse technique to the PBIL and the pure rank-$\mu$ update
CMA-ES and empirically investigate its effect. The experimental results show
that the sample reuse helps to reduce the number of function evaluations on
many benchmark functions for both the PBIL and the pure rank-$\mu$ update
CMA-ES. Moreover, we demonstrate how to combine the importance sampling
technique with a variant of the CMA-ES involving an algorithmic component that
is not derived in the IGO framework.
