A randomized algorithm for continuous optimization

Abstract

The cross entropy (CE) method is a model based search method to solve optimization problems where the objective function has minimal structure. The Monte-Carlo version of the CE method employs the naive sample averaging technique which is inefficient, both computationally and space wise. We provide a novel stochastic approximation version of the CE method, where the sample averaging is replaced with bootstrapping. In our approach, we reuse the previous samples based on discounted averaging, and hence it can save the overall computational and storage cost. Our algorithm is incremental in nature and possesses attractive features such as computational and storage efficiency, accuracy and stability. We provide conditions required for the algorithm to converge to the global optimum. We evaluated the algorithm on a variety of global optimization benchmark problems and the results obtained corroborate our theoretical findings.