On the performance of the Cross-Entropy method

We study the recently introduced Cross-Entropy (CE) method for optimization, an iterative random sampling approach that is based on sampling and updating an underlying distribution function over the set of feasible solutions. In particular, we propose a systematic approach to investigate the convergence and asymptotic convergence rate for the CE method through a novel connection with the well-known stochastic approximation procedures. Extensions of the approach to stochastic optimization will also be discussed.