Assessing solution quality in risk-averse stochastic programs

E. Ruben van Beesten, Nick W. Koning and David P. Morton

Papers from arXiv.org

Abstract: In an optimization problem, 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. Our approach can further make use of existing bias and variance reduction techniques.

Date: 2024-08
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