Joint Optimization for Federated Learning Over the Air

In this paper, we focus on federated learning (FL) over the air based on analog aggregation transmission in realistic wireless networks. We first derive a closed-form expression for the expected convergence rate of FL over the air, which theoretically quantifies the impact of analog aggregation on FL. Based on that, we further develop a joint optimization model for accurate FL implementation, which allows a parameter server to select a subset of edge devices and determine an appropriate power scaling factor. Such a joint optimization of device selection and power control for FL over the air is then formulated as an mixed integer programming problem. Finally, we efficiently solve this problem via a simple finite-set search method. Simulation results show that the proposed solutions developed for wireless channels outperform a benchmark method, and could achieve comparable performance of the ideal case where FL is implemented over reliable and error-free wireless channels.