# Decentralized Consensus Optimization Based on Parallel Random Walk

arXiv: https://arxiv.org/abs/1911.09747 · HTML: https://mlsanity.com/paper/1911.09747/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2019.

## Built on by (most cited first, 5 of 5)

- [Decentralized Federated Learning: Fundamentals, State of the Art, Frameworks, Trends, and Challenges](https://mlsanity.com/paper/2211.08413/) (2022)
- [A Multi-Token Coordinate Descent Method for Semi-Decentralized Vertical Federated Learning](https://mlsanity.com/paper/2309.09977/) (2023)
- [Asynchronous Parallel Incremental Block-Coordinate Descent for Decentralized Machine Learning](https://mlsanity.com/paper/2202.03263/) (2022)
- [Joint Optimization for Federated Learning and Transmission over Unreliable Wireless Networks with Heterogeneous Data](https://mlsanity.com/paper/2609.14246/) (2026)
- [Multi-Token Random-Walk Learning via Meeting-Triggered Information Exchange](https://mlsanity.com/paper/2610.14716/) (2026)

## Abstract (arXiv)

The alternating direction method of multipliers (ADMM) has recently been recognized as a promising approach for large-scale machine learning models. However, very few results study ADMM from the aspect of communication costs, especially jointly with running time. In this letter, we investigate the communication efficiency and running time of ADMM in solving the consensus optimization problem over decentralized networks. We first review the effort of random walk ADMM (W-ADMM), which reduces communication costs at the expense of running time. To accelerate the convergence speed of W-ADMM, we propose the parallel random walk ADMM (PW-ADMM) algorithm, where multiple random walks are active at the same time. Moreover, to further reduce the running time of PW-ADMM, the intelligent parallel random walk ADMM (IPW-ADMM) algorithm is proposed through integrating the textitRandom Walk with Choice with PW-ADMM. By numerical results from simulations, we demonstrate that the proposed algorithms can be both communication efficient and fast in running speed compared with state-of-the-art methods.