Federated learning (FL) is a popular privacy-preserving distributed training scheme, where multiple devices collaborate to train machine learning models by uploading local model updates. To improve communication efficiency, over-the-air computation (AirComp) has been applied to FL, which leverages analog modulation to harness the superposition property of radio waves such that numerous devices can upload their model updates concurrently for aggregation. However, the uplink channel noise incurs considerable model aggregation distortion, which is critically determined by the device scheduling and compromises the learned model performance. In this paper, we propose a probabilistic device scheduling framework for over-the-air FL, named PO-FL, to mitigate the negative impact of channel noise, where each device is scheduled according to a certain probability and its model update is reweighted using this probability in aggregation. We prove the unbiasedness of this aggregation scheme and demonstrate the convergence of PO-FL on both convex and non-convex loss functions. Our convergence bounds unveil that the device scheduling affects the learning performance through the communication distortion and global update variance. Based on the convergence analysis, we further develop a channel and gradient-importance aware algorithm to optimize the device scheduling probabilities in PO-FL. Extensive simulation results show that the proposed PO-FL framework with channel and gradient-importance awareness achieves faster convergence and produces better models than baseline methods.

翻译：联邦学习（FL）是一种流行的隐私保护分布式训练方案，其中多个设备通过上传本地模型更新来协作训练机器学习模型。为提高通信效率，空中计算（AirComp）被应用于FL，它利用模拟调制来利用无线电波的叠加特性，使得大量设备可以同时上传模型更新以进行聚合。然而，上行信道噪声会导致显著的模型聚合失真，该失真关键取决于设备调度，并损害所学习模型的性能。本文提出了一种面向空中FL的概率性设备调度框架，命名为PO-FL，以减轻信道噪声的负面影响，其中每个设备以一定概率被调度，且其模型更新在聚合中使用该概率进行重新加权。我们证明了该聚合方案的无偏性，并展示了PO-FL在凸损失函数和非凸损失函数上的收敛性。我们的收敛界揭示了设备调度通过通信失真和全局更新方差影响学习性能。基于收敛性分析，我们进一步开发了一种信道与梯度重要性感知算法，以优化PO-FL中的设备调度概率。大量仿真结果表明，所提出的具有信道与梯度重要性感知的PO-FL框架比基准方法实现了更快的收敛速度并生成更优的模型。