Over-the-Air Federated Averaging with Limited Power and Privacy Budgets

Abstract

This paper develops an optimal design for device scheduling, alignment coefficient, and aggregation rounds within a differentially private over-the-air federated averaging (DP-OTA-FedAvg) system considering a constrained sum power budget. In DP-OTA-FedAvg, gradients are aligned using an alignment coefficient and then aggregated over the air, utilizing channel noise to ensure participant privacy. This study highlights two critical tradeoffs in aligned over-the-air federated learning (OTA-FL) systems with limited power and privacy budgets. Firstly, it reveals the tradeoff between the number of scheduled devices and the alignment coefficient. Secondly, it investigates the balance between aggregation distortion and local training error while adhering to the sum power constraint. Specifically, we measure privacy using differential privacy (DP) and perform convergence analyses for both convex and non-convex loss functions. These analyses provide insights into how device scheduling, the alignment coefficient, and the number of global aggregations affect both privacy preservation and the learning process. Building on these analytical results, we formulate an optimization problem aimed at minimizing the optimality gap of DP-OTA-FedAvg under power and privacy constraints. By specifying the number of aggregation rounds, we derive a closed-form expression describing the relationship between the alignment coefficient and the number of scheduled devices. We then tackle the problem through iterative optimization of scheduling and aggregation rounds. The effectiveness of the proposed policies is verified through simulations, and the performance advantage is particularly pronounced in scenarios where devices have poor channel conditions and limited sum-power budgets.