  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.
