Domain generalization (DG) and algorithmic fairness are two critical challenges in machine learning. However, most DG methods focus only on minimizing expected risk in the unseen target domain without considering algorithmic fairness. Conversely, fairness methods typically do not account for domain shifts, so the fairness achieved during training may not generalize to unseen test domains. In this work, we bridge these gaps by studying the problem of Fair Domain Generalization (FairDG), which aims to minimize both expected risk and fairness violations in unseen target domains. We derive novel mutual information-based upper bounds for expected risk and fairness violations in multi-class classification tasks with multi-group sensitive attributes. These bounds provide key insights for algorithm design from an information-theoretic perspective. Guided by these insights, we introduce PAFDG (Pareto-Optimal Fairness for Domain Generalization), a practical framework that solves the FairDG problem and models the utility-fairness trade-off through Pareto optimization. Experiments on real-world vision and language datasets show that PAFDG achieves superior utility-fairness trade-offs compared to existing methods.

翻译：域泛化（DG）与算法公平性是机器学习中的两个关键挑战。然而，大多数域泛化方法仅关注最小化未见目标域中的期望风险，而未考虑算法公平性。反之，公平性方法通常未考虑域偏移，因此在训练阶段实现的公平性可能无法泛化至未见测试域。本研究通过探讨公平域泛化（FairDG）问题来弥合这些差距，该问题旨在同时最小化未见目标域中的期望风险与公平性违规。针对具有多组敏感属性的多类别分类任务，我们推导了基于互信息的期望风险与公平性违规的新上界。这些上界从信息论视角为算法设计提供了关键洞见。基于这些洞见，我们提出了PAFDG（面向域泛化的帕累托最优公平性）——一个解决FairDG问题并通过帕累托优化建模效用-公平性权衡的实用框架。在真实世界视觉与语言数据集上的实验表明，相较于现有方法，PAFDG实现了更优的效用-公平性权衡。