Addressing the communication bottleneck inherent in federated learning (FL), over-the-air FL (AirFL) has emerged as a promising solution, which is, however, hampered by deep fading conditions. In this paper, we propose AirFL-Mem, a novel scheme designed to mitigate the impact of deep fading by implementing a \emph{long-term} memory mechanism. Convergence bounds are provided that account for long-term memory, as well as for existing AirFL variants with short-term memory, for general non-convex objectives. The theory demonstrates that AirFL-Mem exhibits the same convergence rate of federated averaging (FedAvg) with ideal communication, while the performance of existing schemes is generally limited by error floors. The theoretical results are also leveraged to propose a novel convex optimization strategy for the truncation threshold used for power control in the presence of Rayleigh fading channels. Experimental results validate the analysis, confirming the advantages of a long-term memory mechanism for the mitigation of deep fading.

提出了一种名为AirFL-Mem的新方案来缓解深衰落对过空中远程联邦学习的影响，并证明了它与理想通信条件下的联邦平均算法(FedAvg)具有相同的收敛速度，而现有方案的性能通常受到误差限制。实验结果验证了长期记忆机制在缓解深衰落方面的优势。

AirFL-Mem: 通过长期记忆改进通信-学习的权衡