Assessing solution quality in risk-averse stochastic programs

Abstract

In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard estimators are optimistically biased, which compromises the statistical guarantee on the optimality gap. We introduce estimators for risk-averse problems that do not suffer from this bias. Our method relies on using two independent samples, each estimating a different component of the optimality gap. Our approach extends a broad class of optimality gap estimation methods from the risk-neutral case to the risk-averse case, such as the multiple replications procedure and its one- and two-sample variants. We show that our approach is tractable and leads to high-quality optimality gap estimates for spectral and quadrangle risk measures. Our approach can further make use of existing bias and variance reduction techniques.