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Accurate Target Privacy Preserving Federated Learning Balancing Fairness and Utility

Kangkang Sun, Jun Wu, Minyi Guo, Jianhua Li, Jianwei Huang

TL;DR

This work tackles the privacy–fairness–utility tension in Federated Learning by formalizing the problem as a multi-objective optimization under differential privacy and fairness constraints. It proposes FedPF, a game-theoretic framework that treats privacy and fairness as competing constraints against model utility, solved via a Learner–Auditor zero-sum interaction and a BEST_F solver for cost-sensitive subproblems. The authors prove an inverse relationship between privacy strength and fairness detectability, and a non-monotonic fairness–utility tradeoff where moderate fairness can improve generalization before over-regularization degrades performance; they also provide an explicit error bound decomposed into Learner Regret, Auditor Regret, and Generalization Error. Empirical results on Adult, Bank, and Compas show up to 42.9% discrimination reduction with competitive accuracy, and the authors release public code at https://github.com/szpsunkk/FedPF to facilitate adoption and further study.

Abstract

Federated Learning (FL) enables collaborative model training without data sharing, yet participants face a fundamental challenge, e.g., simultaneously ensuring fairness across demographic groups while protecting sensitive client data. We introduce a differentially private fair FL algorithm (\textit{FedPF}) that transforms this multi-objective optimization into a zero-sum game where fairness and privacy constraints compete against model utility. Our theoretical analysis reveals a surprising inverse relationship, i.e., stricter privacy protection fundamentally limits the system's ability to detect and correct demographic biases, creating an inherent tension between privacy and fairness. Counterintuitively, we prove that moderate fairness constraints initially improve model generalization before causing performance degradation, where a non-monotonic relationship that challenges conventional wisdom about fairness-utility tradeoffs. Experimental validation demonstrates up to 42.9 % discrimination reduction across three datasets while maintaining competitive accuracy, but more importantly, reveals that the privacy-fairness tension is unavoidable, i.e., achieving both objectives simultaneously requires carefully balanced compromises rather than optimization of either in isolation. The source code for our proposed algorithm is publicly accessible at https://github.com/szpsunkk/FedPF.

Accurate Target Privacy Preserving Federated Learning Balancing Fairness and Utility

TL;DR

This work tackles the privacy–fairness–utility tension in Federated Learning by formalizing the problem as a multi-objective optimization under differential privacy and fairness constraints. It proposes FedPF, a game-theoretic framework that treats privacy and fairness as competing constraints against model utility, solved via a Learner–Auditor zero-sum interaction and a BEST_F solver for cost-sensitive subproblems. The authors prove an inverse relationship between privacy strength and fairness detectability, and a non-monotonic fairness–utility tradeoff where moderate fairness can improve generalization before over-regularization degrades performance; they also provide an explicit error bound decomposed into Learner Regret, Auditor Regret, and Generalization Error. Empirical results on Adult, Bank, and Compas show up to 42.9% discrimination reduction with competitive accuracy, and the authors release public code at https://github.com/szpsunkk/FedPF to facilitate adoption and further study.

Abstract

Federated Learning (FL) enables collaborative model training without data sharing, yet participants face a fundamental challenge, e.g., simultaneously ensuring fairness across demographic groups while protecting sensitive client data. We introduce a differentially private fair FL algorithm (\textit{FedPF}) that transforms this multi-objective optimization into a zero-sum game where fairness and privacy constraints compete against model utility. Our theoretical analysis reveals a surprising inverse relationship, i.e., stricter privacy protection fundamentally limits the system's ability to detect and correct demographic biases, creating an inherent tension between privacy and fairness. Counterintuitively, we prove that moderate fairness constraints initially improve model generalization before causing performance degradation, where a non-monotonic relationship that challenges conventional wisdom about fairness-utility tradeoffs. Experimental validation demonstrates up to 42.9 % discrimination reduction across three datasets while maintaining competitive accuracy, but more importantly, reveals that the privacy-fairness tension is unavoidable, i.e., achieving both objectives simultaneously requires carefully balanced compromises rather than optimization of either in isolation. The source code for our proposed algorithm is publicly accessible at https://github.com/szpsunkk/FedPF.

Paper Structure

This paper contains 27 sections, 2 theorems, 23 equations, 3 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Fairness of FL
  4. Privacy of FL
  5. Tradeoffs among Fairness, Privacy and Utility in FL
  6. Problem Setting and Preliminaries
  7. Federated Learning System Model
  8. Fairness Metrics for Multi-Objective Analysis
  9. Differential Privacy and Fairness Detection Interference
  10. Problem Formulation and Algorithm Design
  11. Optimization Problem in FL
  12. Client-Side Optimization
  13. Server-Side Aggregation
  14. Private and Fair FL Algorithm
  15. Algorithm Design Rationale
  16. ...and 12 more sections

Key Result

Theorem 1

Let $\hat{Y}$ be the output of the FedPF algorithm, and $Y^*$ be the optimal classifier satisfying $(\varepsilon_p, \delta)$-differential privacy (DP) and $\varepsilon_f$-fairness constraints (EO, DemP). If client data are independently and identically distributed and the Rademacher complexity of th where $\mathcal{H} = \ln(1/\delta) \ln^2(8T|\mathcal{A}|/\delta) \log(|\mathcal{K}| + 1)$. $\mathfr

Figures (3)

  • Figure 1: The fairness constraints of FedPF algorithm influence on the discrimination ($\mathcal{G}_{ya}$) without privacy protection in FL.
  • Figure 2: The privacy $\varepsilon_p$ of FedPF algorithm influence on the loss of server model without fairness constraints in FL based on Adult, Bank and Compas datasets, respectively.
  • Figure 3: The privacy budget of FedPF algorithm influence on the loss and the discrimination (EO) of server model in FL based on FedPF algorithm. The fairness constraints include without fairness constraints and With fairness constraints ($\varepsilon_f = 0.1$) lines. The sensitive attributes in Adult, Bank and Compas datasets are Age, Age and Sex, respectively.

Theorems & Definitions (9)

  • Definition 1: Demographic Parity (DemP)
  • Definition 2: Equalized Odds (EO)
  • Definition 3: $\varepsilon_f$-Fair Classifier
  • Definition 4: $\varepsilon_p$-DP for Sensitive Attributes
  • Definition 5: Exponential Mechanism
  • Theorem 1: Privacy-Fairness-Utility Tradeoff of FedPF
  • Proof
  • Theorem 2: Fairness Discrimination Bound of FedPF
  • Proof