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.

本研究提出一种名为PO-FL的概率设备调度框架，以缓解通道噪声的负面影响，在模型对聚合过程中使用该概率重量进行重新加权，通过经验分析得出结论：设备调度通过通信失真和全局更新方差影响学习性能。通过基于收敛性分析，进一步开发了基于渠道和梯度重要性感知的算法，以优化PO-FL中的设备调度概率。广泛的仿真结果表明，基于渠道和梯度重要性感知的PO-FL框架可以实现更快的收敛速度，并产生优于基准方法的模型。

面向无线联邦学习的通道和梯度重要性感知设备调度