A wireless federated learning system is investigated by allowing a server and workers to exchange uncoded information via orthogonal wireless channels. Since the workers frequently upload local gradients to the server via bandwidth-limited channels, the uplink transmission from the workers to the server becomes a communication bottleneck. Therefore, a one-shot distributed principle component analysis (PCA) is leveraged to reduce the dimension of uploaded gradients such that the communication bottleneck is relieved. A PCA-based wireless federated learning (PCA-WFL) algorithm and its accelerated version (i.e., PCA-AWFL) are proposed based on the low-dimensional gradients and the Nesterov's momentum. For the non-convex loss functions, a finite-time analysis is performed to quantify the impacts of system hyper-parameters on the convergence of the PCA-WFL and PCA-AWFL algorithms. The PCA-AWFL algorithm is theoretically certified to converge faster than the PCA-WFL algorithm. Besides, the convergence rates of PCA-WFL and PCA-AWFL algorithms quantitatively reveal the linear speedup with respect to the number of workers over the vanilla gradient descent algorithm. Numerical results are used to demonstrate the improved convergence rates of the proposed PCA-WFL and PCA-AWFL algorithms over the benchmarks.

翻译：本文通过允许服务器与工作节点经由正交无线信道交换未编码信息，对无线联邦学习系统展开研究。由于工作节点需频繁通过带宽受限信道向服务器上传本地梯度，上行传输链路成为通信瓶颈。为此，利用单次分布式主成分分析（PCA）降低上传梯度的维度以缓解通信瓶颈。基于低维梯度与Nesterov动量，提出基于PCA的无线联邦学习算法（PCA-WFL）及其加速版本（PCA-AWFL）。针对非凸损失函数，通过有限时间分析量化系统超参数对PCA-WFL和PCA-AWFL算法收敛性的影响。理论证明PCA-AWFL算法收敛速度快于PCA-WFL算法。此外，PCA-WFL与PCA-AWFL算法的收敛速率定量揭示了相对于原始梯度下降算法，其收敛速度与工作节点数量呈线性加速关系。数值结果验证了所提PCA-WFL与PCA-AWFL算法相比基准方法具有更优的收敛速率。