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

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.

Device Scheduling for Over-the-Air Federated Learning with Differential Privacy

In this paper, we propose a device scheduling scheme for differentially private over-the-air federated learning (DP-OTA-FL) systems, referred to as S-DPOTAFL, where the privacy of the participants is guaranteed by channel noise. In S-DPOTAFL, the gradients are aligned by the alignment coefficient and aggregated via over-the-air computation (AirComp). The scheme schedules the devices with better channel conditions in the training to avoid the problem that the alignment coefficient is limited by the device with the worst channel condition in the system. We conduct the privacy and convergence analysis to theoretically demonstrate the impact of device scheduling on privacy protection and learning performance. To improve the learning accuracy, we formulate an optimization problem with the goal to minimize the training loss subjecting to privacy and transmit power constraints. Furthermore, we present the condition that the S-DPOTAFL performs better than the DP-OTA-FL without considering device scheduling (NoS-DPOTAFL). The effectiveness of the S-DPOTAFL is validated through simulations.

Toward Secure and Private Over-the-Air Federated Learning

In this paper, a novel secure and private over-the-air federated learning (SP-OTA-FL) framework is studied where noise is employed to protect data privacy and system security. Specifically, the privacy leakage of user data and the security level of the system are measured by differential privacy (DP) and mean square error security (MSE-security), respectively. To mitigate the impact of noise on learning accuracy, we propose a channel-weighted post-processing (CWPP) mechanism, which assigns a smaller weight to the gradient of the device with poor channel conditions. Furthermore, employing CWPP can avoid the issue that the signal-to-noise ratio (SNR) of the overall system is limited by the device with the worst channel condition in aligned over-the-air federated learning (OTA-FL). We theoretically analyze the effect of noise on privacy and security protection and also illustrate the adverse impact of noise on learning performance by conducting convergence analysis. Based on these analytical results, we propose device scheduling policies considering privacy and security protection in different cases of channel noise. In particular, we formulate an integer nonlinear fractional programming problem aiming to minimize the negative impact of noise on the learning process. We obtain the closed-form solution to the optimization problem when the model is with high dimension. For the general case, we propose a secure and private algorithm (SPA) based on the branch-and-bound (BnB) method, which can obtain an optimal solution with low complexity. The effectiveness of the proposed CWPP mechanism and the policies for device selection are validated through simulations.