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

TL;DR

This paper proposes a novel over-the-air federated averaging scheme that balances communication efficiency, privacy, and learning performance under power and privacy constraints, with analytical and simulation validation.

Contribution

It introduces a joint design framework for device scheduling, alignment, and aggregation rounds in DP-OTA-FedAvg, optimizing for power and privacy budgets.

Findings

Optimal device scheduling and alignment coefficients improve learning accuracy.

The proposed method effectively balances privacy, power, and convergence speed.

Simulation results confirm the theoretical advantages of the approach.

Abstract

To jointly overcome the communication bottleneck and privacy leakage of wireless federated learning (FL), this paper studies a differentially private over-the-air federated averaging (DP-OTA-FedAvg) system with a limited sum power budget. With DP-OTA-FedAvg, the gradients are aligned by an alignment coefficient and aggregated over the air, and channel noise is employed to protect privacy. We aim to improve the learning performance by jointly designing the device scheduling, alignment coefficient, and the number of aggregation rounds of federated averaging (FedAvg) subject to sum power and privacy constraints. We first present the privacy analysis based on differential privacy (DP) to quantify the impact of the alignment coefficient on privacy preservation in each communication round. Furthermore, to study how the device scheduling, alignment coefficient, and the number of the global aggregation affect the learning process, we conduct the convergence analysis of DP-OTA-FedAvg in the cases of convex and non-convex loss functions. Based on these analytical results, we formulate an optimization problem to minimize the optimality gap of the DP-OTA-FedAvg subject to limited sum power and privacy budgets. The problem is solved by decoupling it into two sub-problems. Given the number of communication rounds, we conclude the relationship between the number of scheduled devices and the alignment coefficient, which offers a set of potential optimal solution pairs of device scheduling and the alignment coefficient. Thanks to the reduced search space, the optimal solution can be efficiently obtained. The effectiveness of the proposed policy is validated through simulations.