A two-time-scale adaptive search algorithm for global optimization

We study a random search algorithm for solving deterministic optimization problems in a black-box scenario. The algorithm has a model-based nature and finds improved solutions by sampling from a distribution model over the feasible region that gradually concentrates its probability mass around high quality solutions. In contrast to many existing algorithms in the class, which are population-based, our approach combines random search with a two-time-scale stochastic approximation idea to address a certain ratio bias inherent in these algorithms and uses only a single candidate solution per iteration. We prove global convergence of the algorithm and carry out numerical experiments to illustrate its performance.