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Over-the-Air Federated Learning in Cell-Free MIMO with Long-term Power Constraint

Yifan Wang, Cheng Zhang, Yuanndon Zhuang, Mingzeng Dai, Haiming Wang, Yongming Huang

TL;DR

The MOP-LOFPC algorithm is introduced, which employs Lyapunov optimization to decouple long-term constraints across rounds while requiring only causal channel state information and achieves a better and more flexible trade-off between the model’s training loss and adherence to long-term power constraints compared to existing baselines.

Abstract

Wireless networks supporting artificial intelligence have gained significant attention, with Over-the-Air Federated Learning emerging as a key application due to its unique transmission and distributed computing characteristics. This paper derives error bounds for Over-the-Air Federated Learning in a Cell-free MIMO system and formulates an optimization problem to minimize optimality gap via joint optimization of power control and beamforming. We introduce the MOP-LOFPC algorithm, which employs Lyapunov optimization to decouple long-term constraints across rounds while requiring only causal channel state information. Experimental results demonstrate that MOP-LOFPC achieves a better and more flexible trade-off between the model's training loss and adherence to long-term power constraints compared to existing baselines.

Over-the-Air Federated Learning in Cell-Free MIMO with Long-term Power Constraint

TL;DR

The MOP-LOFPC algorithm is introduced, which employs Lyapunov optimization to decouple long-term constraints across rounds while requiring only causal channel state information and achieves a better and more flexible trade-off between the model’s training loss and adherence to long-term power constraints compared to existing baselines.

Abstract

Wireless networks supporting artificial intelligence have gained significant attention, with Over-the-Air Federated Learning emerging as a key application due to its unique transmission and distributed computing characteristics. This paper derives error bounds for Over-the-Air Federated Learning in a Cell-free MIMO system and formulates an optimization problem to minimize optimality gap via joint optimization of power control and beamforming. We introduce the MOP-LOFPC algorithm, which employs Lyapunov optimization to decouple long-term constraints across rounds while requiring only causal channel state information. Experimental results demonstrate that MOP-LOFPC achieves a better and more flexible trade-off between the model's training loss and adherence to long-term power constraints compared to existing baselines.
Paper Structure (13 sections, 1 theorem, 19 equations, 3 figures, 1 algorithm)

This paper contains 13 sections, 1 theorem, 19 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Federted Learing Model
  4. Over-the-Air Communication for FL
  5. Problem Formulation
  6. Methodology
  7. MOP Receive Beamforming
  8. LOFPC Power Optimization
  9. Simulation Results
  10. Simulation Setup
  11. Baselines
  12. Results and Discussions
  13. Conclusion

Key Result

Lemma 1

$\left\|\mathbb{E}\left[\boldsymbol{\varepsilon}_t\right]\right\|^2$ and $\mathbb{E}\left(\left\|\boldsymbol{\varepsilon}_{t}\right\|^{2}\right)$ are bounded by (bias) and (mse), respectively, which can be expressed as Proof: By setting $\gamma_t=\sum_{l=1}^Lq\sigma^2(\mathbf{r}_l^{t})^{\rm{H}}\mathbf{r}_l^t$. Based on liu2020privacy, we have the assumption about model bound $\mathbb{E}\left(\lef

Figures (3)

  • Figure 1: Average power versus communication rounds.
  • Figure 2: Loss function versus communication rounds.
  • Figure 3: Loss function versus penalty parameter.

Theorems & Definitions (1)

  • Lemma 1