Joint Optimization of Communications and Federated Learning Over the Air

Federated learning (FL) is an attractive paradigm for making use of rich distributed data while protecting data privacy. Nonetheless, nonideal communication links and limited transmission resources have become the bottleneck of the implementation of fast and accurate FL. In this paper, we study joint optimization of communications and FL 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 the analytical result, we develop a joint optimization model for accurate FL implementation, which allows a parameter server to select a subset of workers and determine an appropriate power scaling factor. Since the practical setting of FL over the air encounters unobservable parameters, we reformulate the joint optimization of worker selection and power allocation using controlled approximation. Finally, we efficiently solve the resulting mixed-integer programming problem via a simple yet optimal finite-set search method by reducing the search space. Simulation results show that the proposed solutions developed for realistic wireless analog channels outperform a benchmark method, and achieve comparable performance of the ideal case where FL is implemented over noise-free wireless channels.