Optimal Allocations for Sample Average Approximation

We consider a single stage stochastic program without recourse with a strictly convex loss function. We assume a compact decision space and grid it with a finite set of points. In addition, we assume that the decision maker can generate samples of the stochastic variable independently at each grid point and form a sample average approximation (SAA) of the stochastic program. Our objective in this paper is to characterize an asymptotically optimal linear sample allocation rule, given a fixed sampling budget, which maximizes the decay rate of probability of making false decision.