多标准决策的鲁棒性分析新框架,更准更可靠。
Scenario theory for multi-criteria data-driven decision making
- 将多个标准的违规风险联合处理,提升鲁棒性评估精度
- 在多个数据集上同时满足多标准的概率更高
- 适合需要多目标决策的复杂系统设计场景
场景方法为不确定性下的数据驱动决策提供了强大框架,具备严格的概率鲁棒性保证。然而,现有理论主要针对单一适用性标准的鲁棒性评估,而许多实际应用(如多智能体决策问题)需要同时考虑多个标准,并基于每个标准对应的独立数据集进行评估。本文建立了通用的多标准数据驱动决策场景理论。核心创新在于对各标准违规风险的联合处理,相比直接套用传统方法,显著提升了鲁棒性证书的准确性。该方法可更精确地量化所有标准同时满足的鲁棒水平。所提框架广泛适用于多标准数据驱动决策问题,提供了一种原理清晰、可扩展且理论严谨的设计方法。
原文摘要 · Abstract (English)
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.
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