Nonconvex sparse learning plays an essential role in many areas, such as signal processing and deep network compression. Iterative hard thresholding (IHT) methods are the state-of-the-art for nonconvex sparse learning due to their capability of recovering true support and scalability with large datasets. Theoretical analysis of IHT is currently based on centralized IID data. In realistic large-scale situations, however, data are distributed, hardly IID, and private to local edge computing devices. It is thus necessary to examine the property of IHT in federated settings, which update in parallel on local devices and communicate with a central server only once in a while without sharing local data. In this paper, we propose two IHT methods: Federated Hard Thresholding (Fed-HT) and Federated Iterative Hard Thresholding (FedIter-HT). We prove that both algorithms enjoy a linear convergence rate and have strong guarantees to recover the optimal sparse estimator, similar to traditional IHT methods, but now with decentralized non-IID data. Empirical results demonstrate that the Fed-HT and FedIter-HT outperform their competitor - a distributed IHT, in terms of decreasing the objective values with lower requirements on communication rounds and bandwidth.

本文提出了两种在联邦学习背景下的非凸稀疏学习迭代算法：Fed-HT和FedIter-HT，证明了它们都具有线性收敛速度和类似于传统IHT方法的优秀稀疏估计保证，同时具有分散的非IID数据。实验结果表明，Fed-HT和FedIter-HT算法在通信轮次和带宽方面都比其竞争对手（分布式IHT）表现优异。

联邦非凸稀疏学习