Scenario theory for multi-criteria data-driven decision making
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914436867948544 |
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| author | Garatti, Simone Manieri, Lucrezia Falsone, Alessandro Carè, Algo Campi, Marco C. Prandini, Maria |
| author_facet | Garatti, Simone Manieri, Lucrezia Falsone, Alessandro Carè, Algo Campi, Marco C. Prandini, Maria |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_00553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scenario theory for multi-criteria data-driven decision making Garatti, Simone Manieri, Lucrezia Falsone, Alessandro Carè, Algo Campi, Marco C. Prandini, Maria Machine Learning Systems and Control Optimization and Control 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. |
| title | Scenario theory for multi-criteria data-driven decision making |
| topic | Machine Learning Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2604.00553 |