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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mehran Poursoltani & Erick Delage & Angelos Georghiou, 2024. "Technical Note—Risk-Averse Regret Minimization in Multistage Stochastic Programs," Operations Research, INFORMS, vol. 72(4), pages 1727-1738, July.
    • Handle: RePEc:inm:oropre:v:72:y:2024:i:4:p:1727-1738
    DOI: 10.1287/opre.2022.2429
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