Discrete stochastic optimization using linear interpolation

We consider discrete stochastic optimization problems where the objective function can only be estimated by a simulation oracle; the oracle is defined only at the discrete points. We propose a method using continuous search with simplex interpolation to solve a wide class of problems. A retrospective framework provides a sequence of deterministic approximating problems that can be solved using continuous optimization techniques that guarantee desirable convergence properties. Numerical experiments show that our method finds the optimal solutions for discrete stochastic optimization problems orders of magnitude faster than existing random search algorithms.