We study federated machine learning at the wireless network edge, where limited power wireless devices, each with its own dataset, build a joint model with the help of a remote parameter server (PS). We consider a bandwidth-limited fading multiple access channel (MAC) from the wireless devices to the PS, and implement distributed stochastic gradient descent (DSGD) over-the-air. We first propose a digital DSGD (D-DSGD) scheme, in which one device is selected opportunistically for transmission at each iteration based on the channel conditions; the scheduled device quantizes its gradient estimate to a finite number of bits imposed by the channel condition, and transmits these bits to the PS in a reliable manner. Next, motivated by the additive nature of the wireless MAC, we propose a novel analog communication scheme, referred to as the compressed analog DSGD (CA-DSGD), where the devices first sparsify their gradient estimates while accumulating error from previous iterations, and project the resultant sparse vector into a low-dimensional vector. We also design a power allocation scheme to align the received gradient vectors at the PS in an efficient manner. Numerical results show that the proposed CA-DSGD algorithm converges much faster than the D-DSGD scheme and other schemes in the literature, while providing a significantly higher accuracy.

本文研究了在无线网络边缘的联邦机器学习，其中有限功率的无线设备，每个设备具有自己的数据集，并利用远程参数服务器（PS）建立联合模型。文章提出了各种技术来实现分布式随机梯度下降（DSGD），其中包括数字DSGD（D-DSGD）和压缩模拟DSGD（CA-DSGD）算法，并通过实验数据表明CA-DSGD算法收敛速度更快，达到更高的精度。

无线衰落信道上的联邦学习