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Fairness-aware Federated Minimax Optimization with Convergence Guarantee

Gerry Windiarto Mohamad Dunda, Shenghui Song

TL;DR

A novel algorithm, fair federated averaging with augmented Lagrangian method (FFALM), designed explicitly to address group fairness issues in FL, is proposed and the theoretical upper bound for the convergence rate of FFALM is derived.

Abstract

Federated learning (FL) has garnered considerable attention due to its privacy-preserving feature. Nonetheless, the lack of freedom in managing user data can lead to group fairness issues, where models are biased towards sensitive factors such as race or gender. To tackle this issue, this paper proposes a novel algorithm, fair federated averaging with augmented Lagrangian method (FFALM), designed explicitly to address group fairness issues in FL. Specifically, we impose a fairness constraint on the training objective and solve the minimax reformulation of the constrained optimization problem. Then, we derive the theoretical upper bound for the convergence rate of FFALM. The effectiveness of FFALM in improving fairness is shown empirically on CelebA and UTKFace datasets in the presence of severe statistical heterogeneity.

Fairness-aware Federated Minimax Optimization with Convergence Guarantee

TL;DR

A novel algorithm, fair federated averaging with augmented Lagrangian method (FFALM), designed explicitly to address group fairness issues in FL, is proposed and the theoretical upper bound for the convergence rate of FFALM is derived.

Abstract

Federated learning (FL) has garnered considerable attention due to its privacy-preserving feature. Nonetheless, the lack of freedom in managing user data can lead to group fairness issues, where models are biased towards sensitive factors such as race or gender. To tackle this issue, this paper proposes a novel algorithm, fair federated averaging with augmented Lagrangian method (FFALM), designed explicitly to address group fairness issues in FL. Specifically, we impose a fairness constraint on the training objective and solve the minimax reformulation of the constrained optimization problem. Then, we derive the theoretical upper bound for the convergence rate of FFALM. The effectiveness of FFALM in improving fairness is shown empirically on CelebA and UTKFace datasets in the presence of severe statistical heterogeneity.
Paper Structure (25 sections, 7 theorems, 23 equations, 2 figures, 3 tables, 1 algorithm)

This paper contains 25 sections, 7 theorems, 23 equations, 2 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Work
  4. Ensuring fairness in centralized learning
  5. Ensuring fairness in FL
  6. Preliminaries
  7. Notations
  8. Group Fairness Metrics
  9. Minimax FL Framework
  10. FFALM
  11. Solving Group Fairness Issue
  12. Problem formulation
  13. Local training phase
  14. Aggregation phase
  15. Theoretical Convergence Guarantee
  16. ...and 10 more sections

Key Result

Theorem 1

Define $\kappa = \frac{L}{\mu}$. Let $\eta_{w,t} = \frac{2\beta^2}{\mu t}$ and $\eta_{\lambda, t} = \mathcal{O}(\frac{1}{t^{2/3}})$. Given that Assumption assumption:boundedvar, Assumption assumption:boundedgrad, and Assumption assumption:lipschitz hold, each $F_{i,S}(w,\lambda)$ is $L$-smooth, each after $T$ communication rounds, where $\Gamma := F_S^* - \sum_{i=1}^N p_i F_{i,S}^*$, $F_S^* := \mi

Figures (2)

  • Figure 1: The minimax FL framework. In each communication round, there are four steps in FL training: 1. Broadcasting phase 2. Local training phase 3. Client-to-server communication phase 4. Aggregation phase.
  • Figure 2: Learning curves on validation set for (a) CelebA dataset and (b) UTKFace dataset

Theorems & Definitions (11)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Theorem 1
  • Lemma 1: lemma7
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • ...and 1 more