A Guide to Sample-Average Approximation

We provide a review of the principle of sample-average approximation (SAA) for solving simulationoptimization problems. Our goal is to provide an accessible overview of the area and emphasize interesting recent work. We explain when one might want to use SAA and when one might expect it to provide good-quality solutions. We also review some of the key theoretical properties of the solutions obtained through SAA. We contrast SAA with stochastic approximation (SA) methods in terms of the computational effort required to obtain solutions of a given quality, explaining why SA “wins” asymptotically. However, an extension of SAA known as retrospective optimization can match the asymptotic convergence rate of SA, at least up to a multiplicative constant.