@article{Zan2026, 
author = {Hao Zan and Dan Chen},
title = {Distributed stochastic optimization algorithm based on Markov sampling},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {4123-4146},
keywords = {distributed stochastic optimization algorithms, variance reduction techniques, Markov chain, resampling methods},
url = {https://www.sciopen.com/article/10.3934/math.2026166},
doi = {10.3934/math.2026166},
abstract = {With the rapid proliferation of big data and high-dimensional datasets, distributed estimation methods have become indispensable for large-scale statistical inference. However, traditional centralized distributed computing frameworks often suffer from communication bottlenecks and privacy risks. To address these challenges, we propose a novel distributed stochastic optimization algorithm, termed gradient-based Markov subsampling Gradient Tracking with Variance Reduction (GMS-GT-VR). This algorithm seamlessly integrates gradient tracking and variance reduction techniques with a data-driven gradient-based Markov subsampling (GMS) strategy to solve large-scale distributed optimization problems over multi-agent networks efficiently. By leveraging a lightweight coordination mechanism for adaptive sampling, GMS-GT-VR effectively reduces both communication overhead and computational complexity, while achieving accelerated convergence. We rigorously establish its theoretical convergence rate of        O    (  1      /    k  ) and conduct a detailed complexity analysis. To validate the theoretical findings, we perform extensive experiments on large-scale datasets. The results consistently demonstrate that GMS-GT-VR outperforms existing variance-reduction methods in terms of communication efficiency and convergence speed, achieving a significant reduction in the number of iterations required.}
}