Reliable Online Decision Making with Covariates

In online decision makings, the challenge often lies in finding the optimal solution quickly based on the covariates observed in real time. In this paper we propose to use the framework of offline simulation and online application to develop algorithms that are capable of solving online simulation optimization problems. In the offline stage, the algorithms solve the optimization problems many times based on different values of the covariates and build predictive models of the optimal solution with respect to the covariates. In the online stage, once the covariates are observed, the optimal solution may be quickly determined by the predictive model. We focus on online strongly convex simulation optimization problems and propose to use different algorithms to construct the predictive models. We derive the rate of convergence of the optimality gaps of the proposed algorithms, and develop a finite-sample statistical measure of the optimality gap when these algorithms are used.