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Global Group Fairness in Federated Learning via Function Tracking

Yves Rychener, Daniel Kuhn, Yifan Hu

TL;DR

This work tackles the challenge of achieving global group fairness in federated learning by introducing a maximum mean discrepancy (MMD) based regularizer paired with a function-tracking scheme that updates the global fairness term without prohibitive communication. The authors derive a client-decomposable gradient estimator for the MMD term, establish a convergence rate for fairness-regularized FedAvg, and reinterpret differential privacy as kernel convolution, enabling DP-aware analysis. They demonstrate, across synthetic and real datasets, that global fairness can be attained with minimal accuracy loss and competitive performance relative to centralized training, while maintaining privacy safeguards. The approach is compatible with standard FL algorithms and offers a principled, scalable solution for enforcing global demographic parity in distributed settings.

Abstract

We investigate group fairness regularizers in federated learning, aiming to train a globally fair model in a distributed setting. Ensuring global fairness in distributed training presents unique challenges, as fairness regularizers typically involve probability metrics between distributions across all clients and are not naturally separable by client. To address this, we introduce a function-tracking scheme for the global fairness regularizer based on a Maximum Mean Discrepancy (MMD), which incurs a small communication overhead. This scheme seamlessly integrates into most federated learning algorithms while preserving rigorous convergence guarantees, as demonstrated in the context of FedAvg. Additionally, when enforcing differential privacy, the kernel-based MMD regularization enables straightforward analysis through a change of kernel, leveraging an intuitive interpretation of kernel convolution. Numerical experiments confirm our theoretical insights.

Global Group Fairness in Federated Learning via Function Tracking

TL;DR

This work tackles the challenge of achieving global group fairness in federated learning by introducing a maximum mean discrepancy (MMD) based regularizer paired with a function-tracking scheme that updates the global fairness term without prohibitive communication. The authors derive a client-decomposable gradient estimator for the MMD term, establish a convergence rate for fairness-regularized FedAvg, and reinterpret differential privacy as kernel convolution, enabling DP-aware analysis. They demonstrate, across synthetic and real datasets, that global fairness can be attained with minimal accuracy loss and competitive performance relative to centralized training, while maintaining privacy safeguards. The approach is compatible with standard FL algorithms and offers a principled, scalable solution for enforcing global demographic parity in distributed settings.

Abstract

We investigate group fairness regularizers in federated learning, aiming to train a globally fair model in a distributed setting. Ensuring global fairness in distributed training presents unique challenges, as fairness regularizers typically involve probability metrics between distributions across all clients and are not naturally separable by client. To address this, we introduce a function-tracking scheme for the global fairness regularizer based on a Maximum Mean Discrepancy (MMD), which incurs a small communication overhead. This scheme seamlessly integrates into most federated learning algorithms while preserving rigorous convergence guarantees, as demonstrated in the context of FedAvg. Additionally, when enforcing differential privacy, the kernel-based MMD regularization enables straightforward analysis through a change of kernel, leveraging an intuitive interpretation of kernel convolution. Numerical experiments confirm our theoretical insights.

Paper Structure

This paper contains 39 sections, 7 theorems, 49 equations, 9 figures, 1 table, 3 algorithms.

Table of Contents

  1. INTRODUCTION
  2. Notation
  3. RELATED WORK
  4. Group Fairness
  5. Federated Learning
  6. Fair Federated Learning
  7. FAIR FEDERATED LEARNING WITH MMD METRICS
  8. ALGORITHM DESIGN
  9. ANALYSIS OF ALGORITHM \ref{['algo:fairfl']}
  10. Convergence Analysis
  11. Differential Privacy
  12. EXPERIMENTS
  13. Synthetic Data
  14. Communities $\&$ Crime Dataset
  15. Compas Dataset
  16. ...and 24 more sections

Key Result

Proposition 3.1

Let $\rho:\mathbb R_+\rightarrow\mathbb R_+$ be a regularization function with $\rho(v)=0$ if and only if $v=0$. Then, there exists no dissimilarity measure $\mathcal{D}:\mathcal{P}(\mathcal{Y})\times\mathcal{P}(\mathcal{Y})\rightarrow\mathbb{R}_+$ satisfying the identity of indiscernibles such that for all $h\in\mathcal{H}$, $\nu_k\geq 0$ with $\sum_{k=1}^K \nu_k=1$ and probability measures $\mat

Figures (9)

  • Figure 1: Illustration of client fairness (red), global group fairness (green) and local group fairness (blue)
  • Figure 2: Performance comparison on synthetic data
  • Figure 3: Performance comparison on real data
  • Figure 4: Performance Comparison on real data
  • Figure 5: Performance for varying $|\mathcal{Y}_0|$ and $|\mathcal{Y}_1|$
  • ...and 4 more figures

Theorems & Definitions (13)

  • Proposition 3.1: Impossibility of Client-Decomposition
  • Definition 3.2: Maximum Mean Discrepancy
  • Lemma 4.1: Unbiased Gradient Estimator
  • Theorem 5.1: Convergence of Algorithm \ref{['algo:fairfl']}
  • Proposition 5.2: Effect of Differential Privacy
  • Corollary 5.3: Differentiable Privacy with Gaussian Kernel
  • Proposition A.1: Generalization Bounds rychener2022metrizing
  • proof : Proof of Proposition \ref{['proposition:decomposition-impossibility']}
  • proof : Proof of Lemma \ref{['lemma:mmd-grad']}
  • Theorem B.3: Convergence Rate of Algorithm \ref{['algo:biased-grads']}
  • ...and 3 more