[2604.00553] Scenario theory for multi-criteria data-driven decision making

Statistics > Machine Learning arXiv:2604.00553 (stat) [Submitted on 1 Apr 2026] Title:Scenario theory for multi-criteria data-driven decision making Authors:Simone Garatti, Lucrezia Manieri, Alessandro Falsone, Algo Carè, Marco C. Campi, Maria Prandini View a PDF of the paper titled Scenario theory for multi-criteria data-driven decision making, by Simone Garatti and 5 other authors View PDF HTML (experimental) 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 da...