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This paper extends scenario theory to multi-criteria data-driven decision making, enabling robust solutions under uncertainty when considering multiple objectives and datasets. By collectively analyzing the risks of violating individual criteria, the authors derive more accurate robustness certificates compared to standard approaches. This leads to a sharper quantification of the robustness level for simultaneous satisfaction of all criteria.
Naively applying standard robustness techniques to multi-criteria decision making yields overly conservative results; this paper offers a tighter analysis that unlocks more practical solutions.
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.