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Over-the-Air Federated Learning via Weighted Aggregation

Seyed Mohammad Azimi-Abarghouyi, Leandros Tassiulas

TL;DR

This work tackles federated learning over fading wireless channels by removing the need for channel state information at transmitters. It introduces WAFeL, a blind over-the-air FL framework that uses adaptive aggregation weights to counteract channel-induced estimation errors, supported by a dedicated receiver architecture. The authors provide a convergence analysis under general loss functions and heterogeneity, and propose two practical weight-selection strategies (MSE minimization and mismatch minimization) with O(K^3) complexity. Experimental results on MNIST and CIFAR-10 show WAFeL achieving notable gains over CSIT-based and CSIT-free schemes, while closely matching ideal error-free performance. The approach offers a scalable, hardware-friendly solution for robust, low-latency FL in wireless edge environments.

Abstract

This paper introduces a new federated learning scheme that leverages over-the-air computation. A novel feature of this scheme is the proposal to employ adaptive weights during aggregation, a facet treated as predefined in other over-the-air schemes. This can mitigate the impact of wireless channel conditions on learning performance, without needing channel state information at transmitter side (CSIT). We provide a mathematical methodology to derive the convergence bound for the proposed scheme in the context of computational heterogeneity and general loss functions, supplemented with design insights. Accordingly, we propose aggregation cost metrics and efficient algorithms to find optimized weights for the aggregation. Finally, through numerical experiments, we validate the effectiveness of the proposed scheme. Even with the challenges posed by channel conditions and device heterogeneity, the proposed scheme surpasses other over-the-air strategies by an accuracy improvement of 15% over the scheme using CSIT and 30% compared to the one without CSIT.

Over-the-Air Federated Learning via Weighted Aggregation

TL;DR

This work tackles federated learning over fading wireless channels by removing the need for channel state information at transmitters. It introduces WAFeL, a blind over-the-air FL framework that uses adaptive aggregation weights to counteract channel-induced estimation errors, supported by a dedicated receiver architecture. The authors provide a convergence analysis under general loss functions and heterogeneity, and propose two practical weight-selection strategies (MSE minimization and mismatch minimization) with O(K^3) complexity. Experimental results on MNIST and CIFAR-10 show WAFeL achieving notable gains over CSIT-based and CSIT-free schemes, while closely matching ideal error-free performance. The approach offers a scalable, hardware-friendly solution for robust, low-latency FL in wireless edge environments.

Abstract

This paper introduces a new federated learning scheme that leverages over-the-air computation. A novel feature of this scheme is the proposal to employ adaptive weights during aggregation, a facet treated as predefined in other over-the-air schemes. This can mitigate the impact of wireless channel conditions on learning performance, without needing channel state information at transmitter side (CSIT). We provide a mathematical methodology to derive the convergence bound for the proposed scheme in the context of computational heterogeneity and general loss functions, supplemented with design insights. Accordingly, we propose aggregation cost metrics and efficient algorithms to find optimized weights for the aggregation. Finally, through numerical experiments, we validate the effectiveness of the proposed scheme. Even with the challenges posed by channel conditions and device heterogeneity, the proposed scheme surpasses other over-the-air strategies by an accuracy improvement of 15% over the scheme using CSIT and 30% compared to the one without CSIT.
Paper Structure (17 sections, 4 theorems, 76 equations, 9 figures, 1 table, 2 algorithms)

This paper contains 17 sections, 4 theorems, 76 equations, 9 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Prior Work
  3. Key Contributions
  4. System Model
  5. Setup
  6. Heterogeneity-Aware Learning Algorithm
  7. WAFeL: Weighted Over-the-Air Scheme
  8. Transmission Scheme
  9. Aggregation Scheme
  10. Convergence Analysis
  11. Aggregation Weight Selection
  12. MSE minimization
  13. Mismatch minimization
  14. Complexity Analysis
  15. Experimental Results
  16. ...and 2 more sections

Key Result

Theorem 1

The optimal equalization vector for a given $\boldsymbol\alpha$, minimizing the MSE in mse, is

Figures (9)

  • Figure 1: Over-the-air FL system. The phase compensation falls within the first quadrant, indicating an imperfect accuracy with a range of $[0,\frac{\pi}{2})$.
  • Figure 2: Receiver architecture at the server.
  • Figure 3: Algorithm 2, MNIST, i.i.d. case.
  • Figure 4: Algorithm 2, MNIST, i.i.d. case.
  • Figure 5: Algorithm 1, MNIST, non-i.i.d. case.
  • ...and 4 more figures

Theorems & Definitions (14)

  • Theorem 1
  • Theorem 2
  • Remark 1
  • Remark 2
  • Corollary 1
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Remark 7
  • ...and 4 more