Scenario theory for multi-criteria data-driven decision making
This work addresses a practical problem in multi-agent decision problems and other applications requiring multiple criteria, offering a principled methodology for design under uncertainty, though it is incremental as it extends existing scenario theory.
The paper tackles the problem of assessing robustness for multi-criteria data-driven decision making under uncertainty, where existing methods focus on single criteria, and develops a scenario theory that provides more accurate robustness certificates, enabling sharper quantification of simultaneous satisfaction of all criteria.
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.