Over-the-Air Federated Learning with Retransmissions (Extended Version)

Motivated by increasing computational capabilities of wireless devices, as well as unprecedented levels of user- and device-generated data, new distributed machine learning (ML) methods have emerged. In the wireless community, Federated Learning (FL) is of particular interest due to its communication efficiency and its ability to deal with the problem of non-IID data. FL training can be accelerated by a wireless communication method called Over-the-Air Computation (AirComp) which harnesses the interference of simultaneous uplink transmissions to efficiently aggregate model updates. However, since AirComp utilizes analog communication, it introduces inevitable estimation errors. In this paper, we study the impact of such estimation errors on the convergence of FL and propose retransmissions as a method to improve FL convergence over resource-constrained wireless networks. First, we derive the optimal AirComp power control scheme with retransmissions over static channels. Then, we investigate the performance of Over-the-Air FL with retransmissions and find two upper bounds on the FL loss function. Finally, we propose a heuristic for selecting the optimal number of retransmissions, which can be calculated before training the ML model. Numerical results demonstrate that the introduction of retransmissions can lead to improved ML performance, without incurring extra costs in terms of communication or computation. Additionally, we provide simulation results on our heuristic which indicate that it can correctly identify the optimal number of retransmissions for different wireless network setups and machine learning problems.