基于最优传输和CVaR的多变量随机优势的可处理松弛

中文摘要 AI 辅助

许多运营决策涉及具有多个不确定属性的备选方案。随机优势避免了对单一多变量效用函数的依赖，但若一个下集或效用比较的排名相反，就会排除精确优势，且多变量优势通常难以验证。我们开发了两种可处理的松弛方法，每种都与随机序的标准表示相关联。首先，补偿随机优势（CSD）松弛了Strassen的耦合刻画：一阶优势要求耦合中几乎处处Q的抽取在每个坐标上都至少是P的抽取，而CSD则允许Q的抽取的选定单调得分在某些耦合对上更低，只要这些得分较低的预期加权量不超过其较高的预期加权量的规定比例。我们证明，一个最优传输问题可计算完整的CSD容忍路径，并通过传输对偶精确刻画生成该序的效用函数，该框架包含替代多变量几乎随机优势（Muller等人，2025）以及一阶和二阶优势之间序的多变量扩展（Muller等人，2017）。其次，参考加权随机优势（RWSD）保留了积分随机序的生成函数，但限制了用于组合其预期效用差的概率测度。我们证明，检查RWSD可简化为条件风险价值（CVaR）问题，并构建了一阶、下正交和递增凹优势的RWSD版本。我们利用传输和CVaR刻画，为CSD和RWSD获得了有限样本统计保证。

英文摘要

Many operational decisions involve alternatives with several uncertain attributes. When comparing such alternatives, stochastic dominance requires every decision maker in a prescribed class to prefer one alternative to the other. These orders have two known limitations: a single extreme decision maker can rule out dominance, and multivariate dominance can be difficult to verify. To address these limitations, we develop two relaxations of their standard representations: compensated stochastic dominance (CSD) relaxes Strassen's coupling representation, while reference-weighted stochastic dominance (RWSD) relaxes the integral representation. We characterize the utility class generated by CSD, recovering known almost stochastic dominance orders as special cases, and characterize it for RWSD in several cases. Importantly, we show that CSD and RWSD can each be checked by computing a single value, an optimal-transport value for CSD and a CVaR value for RWSD, and verifying that this value is nonpositive. This inequality characterization allows us to derive finite-sample guarantees for both orders, even when the outcome dimension is large. An application to Olist e-commerce data shows that, even when empirical FOSD fails, CSD and RWSD quantify how small this failure is and what is needed to overcome it.

发表机构

• National University of Singapore（新加坡国立大学）

机构由 AI 辅助整理，请以论文原文为准。