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

Mehran Poursoltani (), Erick Delage () and Angelos Georghiou ()
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Mehran Poursoltani: GERAD and Department of Decision Sciences, HEC Montréal, Montreal, Quebec H3T 2A7, Canada
Erick Delage: GERAD and Department of Decision Sciences, HEC Montréal, Montreal, Quebec H3T 2A7, Canada
Angelos Georghiou: Department of Business and Public Administration, University of Cyprus, CY-1678 Nicosia, Cyprus

Operations Research, 2024, vol. 72, issue 4, 1727-1738

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 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.

Keywords: Optimization; regret minimization; risk measures; multistage stochastic programming; robust optimization (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:72:y:2024:i:4:p:1727-1738

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