Discrete Convex Simulation Optimization

We propose new sequential simulation algorithms for general convex simulation optimization problems with high-dimensional discrete decision space. The performance of each discrete decision variable is evaluated via stochastic simulation replications. Our proposed simulation algorithms utilize the discrete convex structure and are guaranteed with high probability to find a solution that is close to the best within any given user-specified precision level. The proposed algorithms work for any general convex problem and the efficiency is demonstrated by proved upper bounds on simulation costs. The upper bounds demonstrate a polynomial dependence on the dimension and scale of the decision space. For some discrete simulation optimization problems, a gradient estimator may be available at low costs along with a single simulation replication. By integrating gradient estimators, which are possibly biased, we propose simulation algorithms to achieve optimality guarantees with a reduced dependence on the dimension under moderate assumptions on the bias.