# PMGT-VR: A decentralized proximal-gradient algorithmic framework with variance reduction

arXiv: https://arxiv.org/abs/2012.15010 · HTML: https://mlsanity.com/paper/2012.15010/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2020.

## Built on by (most cited first, 5 of 5)

- [Decentralized Stochastic Variance Reduced Extragradient Method](https://mlsanity.com/paper/2202.00509/) (2022)
- [A Proximal Gradient Method With Probabilistic Multi-Gossip Communications for Decentralized Composite Optimization](https://mlsanity.com/paper/2312.11861/) (2023)
- [Decentralized Stochastic Proximal Gradient Descent with Variance Reduction over Time-varying Networks](https://mlsanity.com/paper/2112.10389/) (2021)
- [Harnessing the Power of Federated Learning in Federated Contextual Bandits](https://mlsanity.com/paper/2312.16341/) (2023)
- [Decentralized Sum-of-Nonconvex Optimization](https://mlsanity.com/paper/2402.02356/) (2024)

## Abstract (arXiv)

This paper considers the decentralized composite optimization problem. We propose a novel decentralized variance-reduction proximal-gradient algorithmic framework, called PMGT-VR, which is based on a combination of several techniques including multi-consensus, gradient tracking, and variance reduction. The proposed framework relies on an imitation of centralized algorithms and we demonstrate that algorithms under this framework achieve convergence rates similar to that of their centralized counterparts. We also describe and analyze two representative algorithms, PMGT-SAGA and PMGT-LSVRG, and compare them to existing state-of-the-art proximal algorithms. To the best of our knowledge, PMGT-VR is the first linearly convergent decentralized stochastic algorithm that can solve decentralized composite optimization problems. Numerical experiments are provided to demonstrate the effectiveness of the proposed algorithms.