Over-the-Air Federated Learning and Optimization

Federated edge learning (FL), as an emerging distributed machine learning paradigm, allows a mass of edge devices to collaboratively train a global model while preserving privacy. In this tutorial, we focus on FL via over-the-air computation (AirComp), which is proposed to reduce the communication overhead for FL over wireless networks at the cost of compromising in the learning performance due to model aggregation error (MAE) arising from channel fading and noise. We first provide a comprehensive study on the convergence of AirCompbased FEDAVG (AirFedAvg) algorithms under both strongly convex (SC) and nonconvex (NC) settings with constant and diminishing learning rates in the presence of data heterogeneity. Through convergence and asymptotic analysis, we characterize the impact of aggregation error on the convergence bound and provide insights for system design with convergence guarantees. Then we derive convergence rates for AirFedAvg algorithms for SC and NC objectives. For different types of local updates that can be transmitted by edge devices (i.e., local model, gradient, and model difference), we reveal that transmitting local model in AirFedAvg may cause divergence in the training procedure. In addition, we consider more practical signal processing schemes to improve the communication efficiency and further extend the convergence analysis to different forms of MAE caused by these signal processing schemes. Extensive simulation results under different settings of objective functions, transmitted local information, and communication schemes verify the theoretical conclusions.