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.

用信息论的视角探讨了联邦学习中与敏感属性（如性别、种族等）相关的公平性权衡问题，通过部分信息分解（PID）的方法确定了三种不公平性的来源，即独特差异、冗余差异和掩盖差异，并在实验证明了这三种差异如何影响全局和本地的公平性，提供了更精细的不公平性来源认知以指导本地差异缓解技术的使用及其在实践中的收敛和效果。