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Updated: Sep 8, 2025

Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface
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PMGT-VR: A Decentralized Proximal-Gradient Algorithmic Framework With Variance Reduction.

Haishan Ye, Wei Xiong, Tong Zhang

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    Summary
    This summary is machine-generated.

    We introduce PMGT-VR, a new decentralized algorithm for composite optimization. It achieves fast convergence rates comparable to centralized methods, offering the first linear convergence for decentralized stochastic composite problems.

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    Area of Science:

    • Optimization Theory
    • Distributed Systems
    • Machine Learning

    Background:

    • Decentralized composite optimization problems are crucial in distributed machine learning and signal processing.
    • Existing decentralized algorithms often suffer from slow convergence or require strong assumptions.
    • Bridging the gap between centralized and decentralized optimization performance is a key challenge.

    Purpose of the Study:

    • To propose a novel decentralized variance-reduction proximal-gradient algorithmic framework (PMGT-VR) for composite optimization.
    • To achieve convergence rates similar to centralized algorithms in a decentralized setting.
    • To introduce the first linearly convergent decentralized stochastic algorithm for this problem class.

    Main Methods:

    • Development of the PMGT-VR framework combining multi-consensus, gradient tracking, and variance reduction.
    • Analysis of two specific algorithms: PMGT-SAGA and PMGT-LSVRG.
    • Comparison with state-of-the-art decentralized proximal algorithms.

    Main Results:

    • The PMGT-VR framework enables decentralized algorithms to mimic centralized convergence rates.
    • PMGT-SAGA and PMGT-LSVRG demonstrate competitive performance against existing methods.
    • PMGT-VR is the first framework to achieve linear convergence for decentralized stochastic composite optimization.

    Conclusions:

    • The proposed PMGT-VR framework significantly advances decentralized optimization.
    • The developed algorithms offer efficient solutions for large-scale distributed problems.
    • Numerical experiments validate the theoretical findings and practical effectiveness.