上海科技大学知识管理系统

Federated Learning (FL) is a promising technique for privacy-preserving edge machine learning. However, it suffers from heavy communication overhead caused by massive edge devices and poor interpretability incurred by black-box deep neural networks. In this paper, we, for the first time, study the statistical optimality of the gradient descent (GD) algorithm in an over-the-air computation (AirComp)-based FL system with shallow neural networks (ShaNNs). Specifically, we propose an AirComp-based FL system that uses polynomial ShaNNs as machine learning models for statistical analysis on edge devices. However, the aggregated gradient is corrupted by the receiver noise of AirComp. To tackle this challenge, we prove that the Frobenius norm of the noise matrix can be bounded if the signal-to-noise ratio and the number of devices are large enough. With this bound, in the first several iterations, the GD trajectory will iterate towards the ground-true point. We also theoretically characterize the estimation gap between the iteration point and the ground-true point. In particular, the GD trajectory will stop iterating towards the ground-true point after some global iterations due to the corruption of noise. Numerical results show that our proposed method enjoys a similar success rate to the noise-free scheme and also verify the proposed theoretical analysis.