将因果模型与个体公平性融入Wasserstein DRO，提升决策鲁棒性。
Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness
- 从因果与个体公平视角重构DRO问题，引入可计算的对偶形式。
- 推导出近似最坏情况损失的闭式正则项，消除极小极大复杂度。
- 适用于需保障公平性且数据分布不确定的机器学习场景。
近年来，Wasserstein分布鲁棒优化（DRO）因其在分布不确定性下的数据驱动决策有效性而受到广泛关注。然而，针对个体公平性、尤其是考虑因果结构和敏感属性的学习问题，相关研究仍十分有限。为此，本文从因果性和个体公平性角度重新建模DRO问题，并提出其对偶形式，将原问题转化为更易处理的计算形式。进一步，我们推导出近似最坏情况损失的闭式表达作为正则项，从而消除原始极小极大问题中的最大化步骤。在更一般情形下，我们实现了该正则项的估计，并探讨了DRO与经典鲁棒优化的关系。最后，在不假设已知结构化因果模型的前提下，我们给出了基于经验分布与估计因果结构设计DRO时的有限样本误差界，确保学习效率与鲁棒性。
原文摘要 · Abstract (English)
In recent years, Wasserstein Distributionally Robust Optimization (DRO) has garnered substantial interest for its efficacy in data-driven decision-making under distributional uncertainty. However, limited research has explored the application of DRO to address individual fairness concerns, particularly when considering causal structures and sensitive attributes in learning problems. To address this gap, we first formulate the DRO problem from causality and individual fairness perspectives. We then present the DRO dual formulation as an efficient tool to convert the DRO problem into a more tractable and computationally efficient form. Next, we characterize the closed form of the approximate worst-case loss quantity as a regularizer, eliminating the max-step in the min-max DRO problem. We further estimate the regularizer in more general cases and explore the relationship between DRO and classical robust optimization. Finally, by removing the assumption of a known structural causal model, we provide finite sample error bounds when designing DRO with empirical distributions and estimated causal structures to ensure efficiency and robust learning.
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