Demystifying Local and Global Fairness Trade-offs in Federated Learning Using Information Theory
Keywords: Fairness, Federated Learning, Machine Learning, Information Theory
Abstract: 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 necessarily 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 real-world 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.
Submission Number: 86
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