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.

翻译：情景方法为不确定性条件下的设计提供了强大的数据驱动框架，并具备严格的概率鲁棒性保证。然而，现有理论主要针对基于数据集评估解决方案的单一适当性准则的鲁棒性，而许多实际应用（包括多智能体决策问题）需要同时考虑多个准则，并基于多个数据集（每个准则对应一个数据集）评估其鲁棒性。本文针对多准则数据驱动决策，提出了一套通用情景理论。其核心创新在于对与各准则违反相关的风险进行集体处理，从而得到比简单套用标准结果更精确的鲁棒性证书。进而，该方法能够更清晰地量化所有准则同时满足的鲁棒性水平。所提出的框架广泛适用于多准则数据驱动决策问题，为不确定性条件下的设计提供了一种原则性强、可扩展且具有坚实理论基础的方法论。