This paper studies the joint device selection and power control scheme for wireless federated learning (FL), considering both the downlink and uplink communications between the parameter server (PS) and the terminal devices. In each round of model training, the PS first broadcasts the global model to the terminal devices in an analog fashion, and then the terminal devices perform local training and upload the updated model parameters to the PS via over-the-air computation (AirComp). First, we propose an AirComp-based adaptive reweighing scheme for the aggregation of local updated models, where the model aggregation weights are directly determined by the uplink transmit power values of the selected devices and which enables the joint learning and communication optimization simply by the device selection and power control. Furthermore, we provide a convergence analysis for the proposed wireless FL algorithm and the upper bound on the expected optimality gap between the expected and optimal global loss values is derived. With instantaneous channel state information (CSI), we formulate the optimality gap minimization problems under both the individual and sum uplink transmit power constraints, respectively, which are shown to be solved by the semidefinite programming (SDR) technique. Numerical results reveal that our proposed wireless FL algorithm achieves close to the best performance by using the ideal FedAvg scheme with error-free model exchange and full device participation.

中文翻译：

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无线联邦学习的联合设备选择和功率控制


本文研究了无线联邦学习（FL）的联合设备选择和功率控制方案，考虑了参数服务器（PS）和终端设备之间的下行和上行通信。在每轮模型训练中，PS首先以模拟方式将全局模型广播到终端设备，然后终端设备进行本地训练并将更新后的模型参数通过空中计算（AirComp）上传到PS 。首先，我们提出了一种基于 AirComp 的自适应重新加权方案，用于聚合本地更新模型，其中模型聚合权重直接由所选设备的上行链路发射功率值确定，并且可以简单地由设备进行联合学习和通信优化选择和功率控制。此外，我们对所提出的无线 FL 算法进行了收敛分析，并推导了预期全局损失值与最佳全局损失值之间的预期最佳性差距的上限。利用瞬时信道状态信息（CSI），我们分别在个体和总上行链路发射功率约束下制定了最优间隙最小化问题，该问题可以通过半定规划（SDR）技术来解决。数值结果表明，我们提出的无线 FL 算法通过使用具有无差错模型交换和完全设备参与的理想 FedAvg 方案，实现了接近最佳性能。