Assessing Solution Quality in Risk-Averse Stochastic Programs

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 standard estimators are optimistically biased for risk-averse problems, 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 methods for estimating the optimality gap from the risk-neutral case to the risk-averse case, such as the multiple replications procedure and its one- and two-sample variants.

About Ruben

Ruben van Beesten is an assistant professor at the Erasmus University Rotterdam and an adjunct professor at the Norwegian University of Science and Technology (NTNU) in Trondheim, Norway. His current research focuses on (1) stochastic programming theory, and (2) energy systems optimization.