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This paper studies the joint device selection and power control scheme forwireless federated learning (FL), considering both the downlink and uplinkcommunications between the parameter server (PS) and the terminal devices. Ineach round of model training, the PS first broadcasts the global model to theterminal devices in an analog fashion, and then the terminal devices performlocal training and upload the updated model parameters to the PS viaover-the-air computation (AirComp). First, we propose an AirComp-based adaptivereweighing scheme for the aggregation of local updated models, where the modelaggregation weights are directly determined by the uplink transmit power valuesof the selected devices and which enables the joint learning and communicationoptimization simply by the device selection and power control. Furthermore, weprovide a convergence analysis for the proposed wireless FL algorithm and theupper bound on the expected optimality gap between the expected and optimalglobal loss values is derived. With instantaneous channel state information(CSI), we formulate the optimality gap minimization problems under both theindividual and sum uplink transmit power constraints, respectively, which areshown to be solved by the semidefinite programming (SDR) technique. Numericalresults reveal that our proposed wireless FL algorithm achieves close to thebest performance by using the ideal FedAvg scheme with error-free modelexchange and full device participation.

Joint Device Selection and Power Control for Wireless Federated Learning