Two-stage nested partitions method for stochastic optimization

We address the problem of optimizing over a large but finite set when the objective function does not have an analytical expression and is evaluated using noisy estimation. Building on the recently proposed nested partitions method for stochastic optimization, we develop a new approach that combines this random search method and statistical selection for guiding the search. We prove asymptotic convergence and analyze the finite time behavior of the new approach. We also report extensive numerical results to illustrate the benefits of the new approach.