Scenario theory for multi-criteria data-driven decision making

• URL: http://arxiv.org/abs/2604.00553v1
• Date: Wed, 01 Apr 2026 06:53:31 GMT
• Title: Scenario theory for multi-criteria data-driven decision making
• Abstract summary: This paper develops a general scenario theory for multi-criteria data-driven decision making.<n>A central innovation lies in the collective treatment of the risks associated with violations of individual criteria.<n>The proposed framework applies broadly to multi-criteria data-driven decision problems.
• Score: 37.58743777054122
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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