Scenario theory for multi-criteria data-driven decision making

2026-04-01

AI Summary

This work addresses the limitation of existing scenario theory, which is confined to single-criterion robustness evaluation and thus ill-suited for real-world decision problems involving multiple criteria that rely on distinct datasets. To overcome this, the paper proposes a general data-driven multi-criteria scenario framework that jointly models violation risks across all criteria, enabling precise quantification of overall robustness guarantees that simultaneously satisfy every criterion. By integrating scenario optimization, probabilistic robustness analysis, and joint risk modeling over multiple datasets, the approach substantially improves the accuracy of robustness certificates. This advancement transcends the constraints of traditional single-criterion methods and offers a theoretically rigorous, scalable, and more accurate framework for delivering joint robustness guarantees in a broad range of multi-criteria decision-making settings.

Abstract

The scenario approach provides a powerful data-driven framework for designing solutions under uncertainty with rigorous probabilistic robustness guarantees. Existing theory, however, primarily addresses assessing robustness with respect to a single appropriateness criterion for the solution based on a dataset, whereas many practical applications - including multi-agent decision problems - require the simultaneous consideration of multiple criteria and the assessment of their robustness based on multiple datasets, one per criterion. This paper develops a general scenario theory for multi-criteria data-driven decision making. A central innovation lies in the collective treatment of the risks associated with violations of individual criteria, which yields substantially more accurate robustness certificates than those derived from a naive application of standard results. In turn, this approach enables a sharper quantification of the robustness level with which all criteria are simultaneously satisfied. The proposed framework applies broadly to multi-criteria data-driven decision problems, providing a principled, scalable, and theoretically grounded methodology for design under uncertainty.

Problem

• multi-criteria decision making
• scenario theory
• robustness guarantees
• data-driven decision making
• uncertainty

Innovation

• scenario theory
• multi-criteria decision making
• data-driven robustness
• probabilistic guarantees
• collective risk treatment