# Decentralized Markov Chain Gradient Descent

arXiv: https://arxiv.org/abs/1909.10238 · HTML: https://mlsanity.com/paper/1909.10238/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2019.

## Built on by (most cited first, 3 of 3)

- [Stability and Generalization for Markov Chain Stochastic Gradient Methods](https://mlsanity.com/paper/2209.08005/) (2022)
- [A Law of Iterated Logarithm for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2110.15092/) (2021)
- [Stability and Generalization of the Decentralized Stochastic Gradient Descent](https://mlsanity.com/paper/2102.01302/) (2021)

## Abstract (arXiv)

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.