EURO 2025 Leeds
Abstract Submission

1517. Regret Robust Optimization: A Generalization with Benchmarks

Invited abstract in session TB-31: Robust and Distributionally Robust Optimization - Theory and Applications, stream Stochastic and Robust optimization.

Tuesday, 10:30-12:00
Room: Maurice Keyworth 1.06

Authors (first author is the speaker)

1. Yannick Becker
2. Pascal Halffmann
Financial Mathematics, Fraunhofer Institute for Industrial Mathematics ITWM
3. Anita Schöbel
Department of Mathematics, University of Kaiserslautern-Landau

Abstract

Decision-makers face challenges due to the inherent uncertainties of real-world scenarios. Robust optimization approaches help to find good decisions across all possible scenarios. While most models require that decisions remain feasible for all scenarios, they often have limitations concerning the optimization objective. For instance, the well-known robust min-max optimization concept tends to overrepresent worst-case scenarios and relies on absolute terms. In contrast, regret robustness approaches focus on comparisons against the best decision that would have been chosen if the scenario was known.

In practice, decision-makers often compare their choices against other market players rather than fictional entities. For a more reliable representation of reality, initial approaches to parametrized regret targets exist in the literature for portfolio optimization. Based on this previous work, we generalize the min-max regret robust optimization concept. We formulate regret with benchmarks independently of any specific application by parametrizing the decision space of the regret target. We present key characteristics of benchmark regret robust solutions and compare them with the standard regret approach and min-max robustness.

This generalized approach can be applied across various domains and provides a practical, reliable framework for practitioners, enabling them to develop strategies better suited to navigate the complexities and uncertainties in decision-making.

Keywords

Status: accepted

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