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.

翻译：为联合解决无线联邦学习（FL）中的通信瓶颈与隐私泄露问题，本文研究了具有有限总功率预算的差分隐私空中联邦平均（DP-OTA-FedAvg）系统。在DP-OTA-FedAvg中，梯度通过对齐系数进行调整并在空中聚合，同时利用信道噪声保护隐私。我们的目标是在总和功率与隐私约束下，通过联合设计设备调度、对齐系数以及联邦平均（FedAvg）的聚合轮数，改善学习性能。我们首先基于差分隐私（DP）进行隐私分析，以量化每轮通信中对齐系数对隐私保护的影响。进一步地，为研究设备调度、对齐系数及全局聚合次数对学习过程的影响，我们分别在凸损失函数与非凸损失函数情形下对DP-OTA-FedAvg进行收敛性分析。基于这些分析结果，我们构建了一个优化问题，旨在最小化有限功率与隐私预算约束下DP-OTA-FedAvg的最优性间隙。该问题通过分解为两个子问题进行求解。在给定通信轮数的条件下，我们推导出调度设备数量与对齐系数之间的关系，从而得出一组潜在的最优设备调度与对齐系数配对解。得益于搜索空间的缩减，可高效获取最优解。仿真结果验证了所提策略的有效性。