2019/09/23 by Tao Sun, Dongsheng Li, Sun, Tao +1
Computer Science · #Distributed Control Multi-Agent Systems #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Privacy-Preserving Technologies in Data #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1909.10238
openalex publication_date 2019/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Decentralized stochastic gradient method emerges as a promising solution for solving large-scale machine learning problems. This paper studies the decentralized Markov chain gradient descent (DMGD) algorithm - a variant of the decentralized stochastic gradient methods where the random samples are taken along the trajectory of a Markov chain. This setting is well-motivated when obtaining independent samples is costly or impossible, which excludes the use of the traditional stochastic gradient algorithms. Specifically, we consider the first- and zeroth-order versions of decentralized Markov chain gradient descent over a connected network, where each node only communicates with its neighbors about intermediate results. The nonergodic convergence and the ergodic convergence rate of the proposed algorithms have been rigorously established, and their critical dependences on the network topology and the mixing time of Markov chain have been highlighted. The numerical tests further validate the sample efficiency of our algorithm.