Discrete optimization via approximate annealing adaptive search with stochastic averaging

We propose a random search algorithm for black-box optimization with discrete decision variables. The algorithm is based on the recently introduced Model-based Annealing Random Search (MARS) for global optimization, which samples candidate solutions from a sequence of iteratively focusing distribution functions over the solution space. In contrast with MARS, which requires a sample size (number of candidate solutions) that grows at least polynomially with the number of iterations for convergence, our approach employs a stochastic averaging idea and uses only a small constant number of candidate solutions per iteration. We establish global convergence of the proposed algorithm and provide numerical examples to illustrate its performance.