[Paper Review] Demystifying Local and Global Fairness Trade-offs in Federated Learning Using Partial Information Decomposition

Faisal Hamman, Sanghamitra Dutta|arXiv (Cornell University)|Jul 21, 2023

Privacy-Preserving Technologies in Data4 citations

TL;DR

This paper introduces a partial information decomposition (PID) framework to analyze and disentangle three distinct sources of unfairness—Unique, Redundant, and Masked Disparity—in federated learning. By formalizing global and local fairness using mutual and conditional mutual information, the authors reveal fundamental trade-offs and limits between local and global fairness, especially under data heterogeneity, and demonstrate through theory and experiments that neither fairness notion implies the other without considering these three disparity components.

ABSTRACT

This work presents 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 often focus on either $ extit{global fairness}$ (overall disparity of the model across all clients) or $ extit{local fairness}$ (disparity of the model at each client), without always considering their trade-offs. There is a lack of understanding regarding the interplay between global and local fairness in FL, particularly under data heterogeneity, 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, $ extit{Unique Disparity}$, $ extit{Redundant Disparity}$, and $ extit{Masked Disparity}$. We demonstrate how these three disparities contribute to global and local fairness using canonical examples. This decomposition helps us derive fundamental limits on the trade-off between global and local fairness, highlighting where they agree or disagree. We introduce the $ extit{Accuracy and Global-Local Fairness Optimality Problem (AGLFOP)}$, a convex optimization that defines the theoretical limits of accuracy and fairness trade-offs, identifying the best possible performance any FL strategy can attain given a dataset and client distribution. We also present experimental results on synthetic datasets and the ADULT dataset to support our theoretical findings.

Motivation & Objective

• To address the lack of understanding in federated learning regarding the interplay between local and global fairness, particularly under data heterogeneity.
• To formalize global and local fairness using information-theoretic measures such as mutual information and conditional mutual information.
• To decompose fairness disparities into three distinct components—Unique, Redundant, and Masked Disparity—using partial information decomposition (PID).
• To derive fundamental information-theoretic limits and trade-offs between local and global fairness.
• To provide empirical validation of the PID framework using benchmark datasets under varying sensitive attribute distributions and synergy levels.

Proposed method

• Formalize global fairness as the mutual information I(Z;Ŷ), where Z is the sensitive attribute and Ŷ is the model prediction.
• Define local fairness as the conditional mutual information I(Z;Ŷ|S), where S denotes the client identity.
• Apply partial information decomposition (PID) to decompose I(Z;Ŷ) and I(Z;Ŷ|S) into three components: Unique Disparity, Redundant Disparity, and Masked Disparity.
• Use canonical examples to illustrate how each disparity component contributes to global and local unfairness in different data distribution scenarios.
• Conduct experiments on benchmark datasets (e.g., Adult) with varying sensitive attribute distributions (α) and synergy levels (λ) to quantify the three disparity components.
• Analyze results across two-client and multi-client (K=10) settings to validate theoretical trade-offs and the presence of all three disparity types under realistic data heterogeneity.

Experimental results

Research questions

• RQ1 How do global and local fairness in federated learning interrelate, and under what conditions does one imply the other?
• RQ2 What are the fundamental information-theoretic limits on achieving fairness when data is non-i.i.d. across clients?
• RQ3 How do Unique, Redundant, and Masked Disparity contribute to global and local unfairness in federated learning?
• RQ4 To what extent does data heterogeneity in sensitive attributes affect the decomposition of fairness disparities?
• RQ5 How do synergy levels between the sensitive attribute and client identity influence the magnitude of Masked Disparity?

Key findings

• Under data heterogeneity, global fairness cannot guarantee local fairness due to the presence of Redundant Disparity, which captures the portion of unfairness that is shared across clients but not captured by individual client models.
• Local fairness does not imply global fairness due to Masked Disparity, which represents the synergistic unfairness arising from the interaction between the sensitive attribute and client identity, not captured by local or global measures alone.
• When sensitive attribute distributions are balanced (α=0.33), only Unique Disparity remains, indicating that fairness trade-offs are most pronounced under imbalanced data.
• As synergy levels (λ) between Z and S increase, Masked Disparity grows significantly—reaching 0.1644 at λ=1—demonstrating that high synergy can lead to substantial hidden unfairness.
• In multi-client settings (K=10), all three disparity types are observable, especially when data is near-i.i.d., confirming the framework's relevance in realistic federated settings.
• The PID framework reveals that Unique Disparity is the only component that can be directly mitigated via local fairness techniques, while Redundant and Masked Disparities require global coordination or architectural adjustments.