Scenario theory for multi-criteria data-driven decision making

TL;DR

This paper extends scenario theory to multi-criteria decision making, enabling more accurate robustness guarantees across multiple datasets and criteria in data-driven uncertain environments.

Contribution

It introduces a collective risk treatment approach for multiple criteria, improving robustness certificates and enabling sharper multi-criteria robustness quantification.

Findings

More accurate robustness certificates for multiple criteria.

Enhanced robustness quantification across datasets.

Broad applicability to multi-criteria decision problems.

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.