Risk-averse Regret Minimization in Multi-stage Stochastic Programs

Mehran Poursoltani(mehran.poursoltanihec.ca)
Erick Delage(erick.delagehec.ca)
Angelos Georghiou(georghiou.angelosucy.ac.cy)

Abstract: 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 multi-stage 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 Delta steps into the future. The Delta-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 Delta-regret minimizing solutions.

Keywords: Regret minimization, risk measures, multi-stage stochastic programming, robust optimization

Category 1: Stochastic Programming

Category 2: Robust Optimization

Category 3: Applications -- OR and Management Sciences

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Entry Submitted: 12/11/2021
Entry Accepted: 12/11/2021
Entry Last Modified: 12/11/2021

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