In this paper, we present an information-theoretic perspective to group fairness trade-offs in federated learning (FL) with respect to sensitive attributes, such as gender, race, etc. Existing works mostly focus on either \emph{global fairness} (overall disparity of the model across all clients) or \emph{local fairness} (disparity of the model at each individual client), without always considering their trade-offs. There is a lack of understanding of the interplay between global and local fairness in FL, and if and when one implies the other. To address this gap, we leverage a body of work in information theory called partial information decomposition (PID) which first identifies three sources of unfairness in FL, namely, \emph{Unique Disparity}, \emph{Redundant Disparity}, and \emph{Masked Disparity}. Using canonical examples, we demonstrate how these three disparities contribute to global and local fairness. This decomposition helps us derive fundamental limits and trade-offs between global or local fairness, particularly under data heterogeneity, as well as, derive conditions under which one implies the other. We also present experimental results on benchmark datasets to support our theoretical findings. This work offers a more nuanced understanding of the sources of disparity in FL that can inform the use of local disparity mitigation techniques, and their convergence and effectiveness when deployed in practice.

翻译：本文提出了一种信息论视角，用于分析联邦学习中与敏感属性（如性别、种族等）相关的群体公平性权衡问题。现有研究主要关注全局公平性（模型在所有客户端上的整体差异）或局部公平性（模型在单个客户端上的差异），但较少考虑两者之间的权衡关系。目前对联邦学习中全局与局部公平性之间的相互作用、以及两者是否相互蕴含的条件缺乏深入理解。为填补这一空白，我们借助信息论中的"部分信息分解"理论框架，首次识别出联邦学习中三种不公平性来源：唯一差异、冗余差异和掩蔽差异。通过典型示例，我们阐明了这三种差异如何影响全局与局部公平性。该分解方法不仅推导出全局与局部公平性之间的基本极限与权衡关系（尤其在数据异构条件下），还揭示了二者相互蕴含的边界条件。我们在基准数据集上的实验结果进一步验证了理论发现。本研究为理解联邦学习中差异来源提供了更精细的视角，可为局部差异缓解技术的实际部署、收敛性及有效性评估提供理论指导。