Improving Sample Average Approximation Using Distributional Robustness

Sample average approximation is a popular approach to solving stochastic optimization problems. It has been widely observed that some form of robustification of these problems often improves the out-of-sample performance of the solution estimators. In estimation problems, this improvement boils down to a trade-off between the opposing effects of bias and shrinkage. This paper aims to characterize the features of more general optimization problems that exhibit this behaviour when a distributionally robust version of the sample average approximation problem is used. The paper restricts attention to quadratic problems for which sample average approximation solutions are unbiased and shows that expected out-of-sample performance can be calculated for small amounts of robustification and depends on the type of distributionally robust model used and properties of the underlying ground-truth probability distribution of random variables. The paper was written as part of a New Zealand funded research project that aimed to improve stochastic optimization methods in the electric power industry. The authors of the paper have worked together in this domain for the past 25 years.