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Age-Aware Edge-Blind Federated Learning via Over-the-Air Aggregation

Ahmed M. Elshazly, Ahmed Arafa

TL;DR

A convergence bound is provided that highlights the advantages of using a higher number of antenna array elements and demonstrates a key trade-off: increasing \(k\) decreases compression error at the cost of increasing the effect of channel noise.

Abstract

We study federated learning (FL) over wireless fading channels where multiple devices simultaneously send their model updates. We propose an efficient \emph{age-aware edge-blind over-the-air FL} approach that does not require channel state information (CSI) at the devices. Instead, the parameter server (PS) uses multiple antennas and applies maximum-ratio combining (MRC) based on its estimated sum of the channel gains to detect the parameter updates. A key challenge is that the number of orthogonal subcarriers is limited; thus, transmitting many parameters requires multiple Orthogonal Frequency Division Multiplexing (OFDM) symbols, which increases latency. To address this, the PS selects only a small subset of model coordinates each round using \emph{AgeTop-\(k\)}, which first picks the largest-magnitude entries and then chooses the \(k\) coordinates with the longest waiting times since they were last selected. This ensures that all selected parameters fit into a single OFDM symbol, reducing latency. We provide a convergence bound that highlights the advantages of using a higher number of antenna array elements and demonstrates a key trade-off: increasing \(k\) decreases compression error at the cost of increasing the effect of channel noise. Experimental results show that (i) more PS antennas greatly improve accuracy and convergence speed; (ii) AgeTop-\(k\) outperforms random selection under relatively good channel conditions; and (iii) the optimum \(k\) depends on the channel, with smaller \(k\) being better in noisy settings.

Age-Aware Edge-Blind Federated Learning via Over-the-Air Aggregation

TL;DR

A convergence bound is provided that highlights the advantages of using a higher number of antenna array elements and demonstrates a key trade-off: increasing decreases compression error at the cost of increasing the effect of channel noise.

Abstract

We study federated learning (FL) over wireless fading channels where multiple devices simultaneously send their model updates. We propose an efficient \emph{age-aware edge-blind over-the-air FL} approach that does not require channel state information (CSI) at the devices. Instead, the parameter server (PS) uses multiple antennas and applies maximum-ratio combining (MRC) based on its estimated sum of the channel gains to detect the parameter updates. A key challenge is that the number of orthogonal subcarriers is limited; thus, transmitting many parameters requires multiple Orthogonal Frequency Division Multiplexing (OFDM) symbols, which increases latency. To address this, the PS selects only a small subset of model coordinates each round using \emph{AgeTop-}, which first picks the largest-magnitude entries and then chooses the coordinates with the longest waiting times since they were last selected. This ensures that all selected parameters fit into a single OFDM symbol, reducing latency. We provide a convergence bound that highlights the advantages of using a higher number of antenna array elements and demonstrates a key trade-off: increasing decreases compression error at the cost of increasing the effect of channel noise. Experimental results show that (i) more PS antennas greatly improve accuracy and convergence speed; (ii) AgeTop- outperforms random selection under relatively good channel conditions; and (iii) the optimum depends on the channel, with smaller being better in noisy settings.
Paper Structure (9 sections, 1 theorem, 36 equations, 3 figures, 1 algorithm)

This paper contains 9 sections, 1 theorem, 36 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Federated Learning Model
  4. Age-Aware Over-the-Air Communication Model
  5. Convergence Analysis
  6. Preliminaries
  7. Convergence Rate
  8. Experimental Results and Discussion
  9. Conclusion

Key Result

Theorem 1

Let $0 < \eta(t) \le \min\!\left\{ 1, \frac{1}{\mu \tau} \right\}, \; \forall t$. Under Assumptions 1--5, we have The terms $D(i)$ and $Q(i)$ are defined as follows:

Figures (3)

  • Figure 1: Performance with different number of antennas $N$.
  • Figure 2: AgeTop-k versus rTop-k under relatively good channel conditions.
  • Figure 3: Performance with different compression values $k$.

Theorems & Definitions (2)

  • Theorem 1
  • proof : Proof Sketch