Federated Learning over Noisy Channels

Does Federated Learning (FL) work when both uplink and downlink communications have errors? How much communication noise can FL handle and what is its impact to the learning performance? This work is devoted to answering these practically important questions by explicitly incorporating both uplink and downlink noisy channels in the FL pipeline. We present a rigorous convergence analysis of FL over simultaneous uplink and downlink noisy communication channels, and characterize the sufficient conditions for FL to maintain the same convergence rate scaling as the ideal case of no communication error. The analysis reveals that, in order to maintain the $\mathcal{O}\left( {1/T} \right)$ convergence rate of FedAvg with perfect communications, the uplink and downlink signal-to-noise-ratio (SNR) should be controlled such that they scale as $\mathcal{O}\left( {{t^2}} \right)$ where t is the index of communication rounds. This key result leads to a transmit power control policy for analog aggregation, whose performance is shown to be superior over the standard method via extensive numerical experiments using real-world FL tasks.