CONFIDENCE SETS FOR DISCRETE STOCHASTIC OPTIMIZATION

Consider the problem of finding the points of maximum of an expectation functional over a finite set S. Based on statistical estimates at each point of S, confidence sets for the argmax-set are constructed which guarantee a prespecified probability of correct selection. We review known selection methods and propose a new two-stage procedure that works well for large S and few global maxima. The performance is compared in a simulation study.