Boosting Fairness and Robustness in Over-the-Air Federated Learning

TL;DR

Addressing fairness and robustness in over-the-air federated learning with unknown wireless channels, the paper formulates a minimax objective across agents and derives an epigraph reformulation with a penalty term $ \min_{\theta \in \Theta} \max_{i\in V} g_i(\theta)$ and $ \min_{\alpha} \alpha$ s.t. $ g_i(\theta) \le \alpha$. The FedFAir algorithm operates over a WMAC channel without channel reconstruction, weighting client updates by $h_i(k) = \lambda_i(k)/\sum_j \lambda_j(k)$ and proving almost-sure convergence to the minimax optimum. Empirical results on federated logistic regression demonstrate superior fairness and accuracy under data heterogeneity and significant communication-efficiency gains compared with TDMA-based FedAVG. The work enables scalable, privacy-preserving, robust FL for beyond-5G networks, reducing overhead while ensuring worst-case performance guarantees.

Abstract

Over-the-Air Computation is a beyond-5G communication strategy that has recently been shown to be useful for the decentralized training of machine learning models due to its efficiency. In this paper, we propose an Over-the-Air federated learning algorithm that aims to provide fairness and robustness through minmax optimization. By using the epigraph form of the problem at hand, we show that the proposed algorithm converges to the optimal solution of the minmax problem. Moreover, the proposed approach does not require reconstructing channel coefficients by complex encoding-decoding schemes as opposed to state-of-the-art approaches. This improves both efficiency and privacy.

Figures (2)

• Figure 1: Comparison of the performances FedFAir and FedAVG algorithms on unseen data during training in terms of their accuracy.
• Figure 2: Comparison of Confusion Matrices

Theorems & Definitions (6)

• Lemma 1: bartle2000introduction
• Lemma 2: polyak1987introduction
• Lemma 3: alber1998projected
• Lemma 4
• Theorem 1
• proof