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September 10, 2025

PMGT-VR: a Decentralized Proximal-gradient Algorithmic Framework with Variance Reduction

Puntos clave

PMGT-VR achieves linearly convergent results in decentralized optimization, enhancing efficiency in problem-solving.
The effectiveness of PMGT-SAGA and PMGT-LSVRG is demonstrated through comparative analysis with state-of-the-art algorithms.
A novel algorithmic framework that incorporates variance reduction techniques provides significant improvements in optimization.
Numerical experiments validate the proposed methods, suggesting practical applications in decentralized settings.

Resumen

This paper considers the decentralized composite optimization problem. We propose a novel decentralized variance-reduction proximal-gradient algorithmic framework, called PMGT-VR, which combines several techniques, including multi-consensus, gradient tracking, and variance reduction. The proposed framework imitates centralized algorithms and 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.

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