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The Cost of Local and Global Fairness in Federated Learning

Yuying Duan, Gelei Xu, Yiyu Shi, Michael Lemmon

TL;DR

The paper addresses fairness in federated learning for multi-class problems by jointly enforcing global and local equalized odds via a post-processing LP built on a region-under-ROC-surface framework. It introduces a Bayesian optimal score function, derives a post-processing predictor through an LP over true-positive rates, and uses a simplex-based inner approximation to enable scalable optimization in FL; a linear-algebraic equation (LAE) then yields a randomized fair predictor that preserves accuracy within the specified fairness constraints. The approach yields an epsilon-fair optimal predictor with polynomial-time complexity and demonstrates superior fairness-accuracy trade-offs and reduced communication and computation costs compared to state-of-the-art baselines on real datasets (Adult, ACSPublicCoverage, HM10000). It also analyzes data heterogeneity and privacy implications, showing predictable behavior under non-i.i.d. data and differential privacy budgets. Overall, the framework provides a practical and theoretically grounded method to deploy fair multi-class FL with controllable fairness levels and efficiency gains.

Abstract

With the emerging application of Federated Learning (FL) in finance, hiring and healthcare, FL models are regulated to be fair, preventing disparities with respect to legally protected attributes such as race or gender. Two concepts of fairness are important in FL: global and local fairness. Global fairness addresses the disparity across the entire population and local fairness is concerned with the disparity within each client. Prior fair FL frameworks have improved either global or local fairness without considering both. Furthermore, while the majority of studies on fair FL focuses on binary settings, many real-world applications are multi-class problems. This paper proposes a framework that investigates the minimum accuracy lost for enforcing a specified level of global and local fairness in multi-class FL settings. Our framework leads to a simple post-processing algorithm that derives fair outcome predictors from the Bayesian optimal score functions. Experimental results show that our algorithm outperforms the current state of the art (SOTA) with regard to the accuracy-fairness tradoffs, computational and communication costs. Codes are available at: https://github.com/papersubmission678/The-cost-of-local-and-global-fairness-in-FL .

The Cost of Local and Global Fairness in Federated Learning

TL;DR

The paper addresses fairness in federated learning for multi-class problems by jointly enforcing global and local equalized odds via a post-processing LP built on a region-under-ROC-surface framework. It introduces a Bayesian optimal score function, derives a post-processing predictor through an LP over true-positive rates, and uses a simplex-based inner approximation to enable scalable optimization in FL; a linear-algebraic equation (LAE) then yields a randomized fair predictor that preserves accuracy within the specified fairness constraints. The approach yields an epsilon-fair optimal predictor with polynomial-time complexity and demonstrates superior fairness-accuracy trade-offs and reduced communication and computation costs compared to state-of-the-art baselines on real datasets (Adult, ACSPublicCoverage, HM10000). It also analyzes data heterogeneity and privacy implications, showing predictable behavior under non-i.i.d. data and differential privacy budgets. Overall, the framework provides a practical and theoretically grounded method to deploy fair multi-class FL with controllable fairness levels and efficiency gains.

Abstract

With the emerging application of Federated Learning (FL) in finance, hiring and healthcare, FL models are regulated to be fair, preventing disparities with respect to legally protected attributes such as race or gender. Two concepts of fairness are important in FL: global and local fairness. Global fairness addresses the disparity across the entire population and local fairness is concerned with the disparity within each client. Prior fair FL frameworks have improved either global or local fairness without considering both. Furthermore, while the majority of studies on fair FL focuses on binary settings, many real-world applications are multi-class problems. This paper proposes a framework that investigates the minimum accuracy lost for enforcing a specified level of global and local fairness in multi-class FL settings. Our framework leads to a simple post-processing algorithm that derives fair outcome predictors from the Bayesian optimal score functions. Experimental results show that our algorithm outperforms the current state of the art (SOTA) with regard to the accuracy-fairness tradoffs, computational and communication costs. Codes are available at: https://github.com/papersubmission678/The-cost-of-local-and-global-fairness-in-FL .

Paper Structure

This paper contains 26 sections, 5 theorems, 93 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminary Definitions
  4. Region under the ROC Surface
  5. The Minimum Cost of Fairness
  6. Training Fair Predictor in FL
  7. Experiments
  8. Conclusions
  9. Acknowledgments
  10. The Parameters of Convex Program in Proposition \ref{['prop:convex_program']}
  11. The Parameters of Simplex $\widehat{D_{ac}}$
  12. The Parameters of LAE in Proposition \ref{['prop:uniqueness']}
  13. Extension to Other Fairness Metrics (Equal Opportunity and Statistical Parity)
  14. Equal Opportunity
  15. Statistical Parity
  16. ...and 11 more sections

Key Result

Proposition 4.3

(Appendix app:proof_NP_multi_class) Consider client $c$ and group $a$, let $\{\widetilde{Y}_{\boldsymbol{\theta}}\}_{\boldsymbol{\theta} \in \mathbb{R}^N_{\geq 0}}$ be the set of all derived outcome predictors, and let $\{\phi_g\}_{g=1}^{N-1}, \in [0,1]^N$ be a set of specified values of true positi then $\widetilde{Y}^* \in \{\widetilde{Y}_{\boldsymbol{\theta}}\}_{\boldsymbol{\theta} \in \mathbb{

Figures (2)

  • Figure 1: The accuracy under different levels of local fairness (y-axis) and global fairness (x-axis). The numbers inside the blocks are the accuracy, with each value being the average of 10 runs.
  • Figure 2: The accuracy under different levels of local (y-axis) and global fairness (x-axis) for different data heterogeneity setup of HM10000. (each value is the average of 10 runs.)

Theorems & Definitions (16)

  • Definition 3.1
  • Definition 3.2
  • Definition 3.3
  • Definition 4.1: Bayesian Optimal Score Function
  • Definition 4.2: Derived Outcome Predictor
  • Proposition 4.3
  • Definition 4.4
  • Definition 4.5
  • Proposition 4.6
  • Proposition 4.7
  • ...and 6 more