Risk-Averse Regret Minimization in Multistage Stochastic Programs

Abstract

Regret minimization has gained popularity in a wide range of decision-making problems under uncertainty because of its capacity to identify more opportunistic solutions than worst-case value optimization. Unfortunately, the rigidity of current worst-case regret models and scarcity of tractable solution methods have been serious obstacles in multistage applications. In “Risk-Averse Regret Minimization in Multistage Stochastic Programs,” M. Poursoltani, E. Delage, and A. Georghiou consider a multistage stochastic programming setting with a discrete scenario tree. They introduce the notion of the Δ-regret model, which bridges between the ex ante and ex post regret minimization paradigms that are currently used in the regret minimization literature for single-stage problems. The notion of Δ-regret minimization is investigated for the first time both theoretically and numerically in order to better understand its behavior under a set of popular risk measures.