Technical Note—Risk-Averse Regret Minimization in Multistage Stochastic Programs.

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. Within the context of optimization under uncertainty, a well-known alternative to minimizing expected value or the worst-case scenario consists in minimizing regret. In a multistage stochastic programming setting with a discrete probability distribution, we explore the idea of risk-averse regret minimization, where the benchmark policy can only benefit from foreseeing Δ steps into the future. The Δ-regret model naturally interpolates between the popular ex ante and ex post regret models. We provide theoretical and numerical insights about this family of models under popular coherent risk measures and shed new light on the conservatism of the Δ-regret minimizing solutions. Funding: This work was supported by Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2016-05208], the Canada Research Chair program [Grant 950-230057], and the Fonds de recherche du Québec–Nature et technologies [Grant 271693]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2022.2429. [ABSTRACT FROM AUTHOR]