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

TL;DR

This paper introduces PMGT-VR, a novel decentralized variance-reduction proximal-gradient framework that achieves convergence rates comparable to centralized algorithms for decentralized composite optimization problems.

Contribution

It presents the first linearly convergent decentralized stochastic algorithm for solving decentralized composite optimization problems, combining multiple advanced techniques.

Findings

Achieves convergence rates similar to centralized algorithms.

Demonstrates effectiveness through numerical experiments.

Introduces two specific algorithms: PMGT-SAGA and PMGT-LSVRG.

Abstract

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.