# Federated Nonconvex Sparse Learning

arXiv: https://arxiv.org/abs/2101.00052 · HTML: https://mlsanity.com/paper/2101.00052/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2020.

## Built on by (most cited first, 10 of 10)

- [Federated Learning via Inexact ADMM](https://mlsanity.com/paper/2204.10607/) (2022)
- [On Convergence of FedProx: Local Dissimilarity Invariant Bounds, Non-smoothness and Beyond](https://mlsanity.com/paper/2206.05187/) (2022)
- [Communication-Efficient ADMM-based Federated Learning](https://mlsanity.com/paper/2110.15318/) (2021)
- [Non-IID data in Federated Learning: A Survey with Taxonomy, Metrics, Methods, Frameworks and Future Directions](https://mlsanity.com/paper/2411.12377/) (2024)
- [Federated Data Analytics: A Study on Linear Models](https://mlsanity.com/paper/2206.07786/) (2022)
- [FedGiA: An Efficient Hybrid Algorithm for Federated Learning](https://mlsanity.com/paper/2205.01438/) (2022)
- [Federated Gradient Matching Pursuit](https://mlsanity.com/paper/2302.10755/) (2023)
- [Federated Composite Saddle Point Optimization](https://mlsanity.com/paper/2305.15643/) (2023)
- [Equitable-FL: Federated Learning with Sparsity for Resource-Constrained Environment](https://mlsanity.com/paper/2309.00864/) (2023)
- [Sparse-ProxSkip: Accelerated Sparse-to-Sparse Training in Federated Learning](https://mlsanity.com/paper/2405.20623/) (2024)

## Abstract (arXiv)

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.