Leveraging over-the-air computations for model aggregation is an effective approach to cope with the communication bottleneck in federated edge learning. By exploiting the superposition properties of multi-access channels, this approach facilitates an integrated design of communication and computation, thereby enhancing system privacy while reducing implementation costs. However, the inherent electromagnetic interference in radio channels often exhibits heavy-tailed distributions, giving rise to exceptionally strong noise in globally aggregated gradients that can significantly deteriorate the training performance. To address this issue, we propose a novel gradient clipping method, termed Median Anchored Clipping (MAC), to combat the detrimental effects of heavy-tailed noise. We also derive analytical expressions for the convergence rate of model training with analog over-the-air federated learning under MAC, which quantitatively demonstrates the effect of MAC on training performance. Extensive experimental results show that the proposed MAC algorithm effectively mitigates the impact of heavy-tailed noise, hence substantially enhancing system robustness.

翻译：利用空中计算进行模型聚合是应对联邦边缘学习中通信瓶颈的有效方法。该方法通过利用多址信道的叠加特性，促进了通信与计算的集成设计，从而在降低实现成本的同时增强了系统隐私性。然而，无线电信道中固有的电磁干扰通常呈现重尾分布，导致全局聚合梯度中出现异常强烈的噪声，可能显著恶化训练性能。为解决此问题，我们提出了一种新颖的梯度截断方法，称为中值锚定截断（MAC），以对抗重尾噪声的有害影响。我们还推导了在MAC下采用模拟空中联邦学习的模型训练收敛速率的解析表达式，定量展示了MAC对训练性能的影响。大量实验结果表明，所提出的MAC算法能有效缓解重尾噪声的影响，从而显著增强系统鲁棒性。