# Linearly Convergent Asynchronous Distributed ADMM via Markov Sampling

arXiv: https://arxiv.org/abs/1810.05067 · HTML: https://mlsanity.com/paper/1810.05067/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2018.

## 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)
- [Mobilizing Personalized Federated Learning in Infrastructure-Less and Heterogeneous Environments via Random Walk Stochastic ADMM](https://mlsanity.com/paper/2304.12534/) (2023)
- [Stability and Generalization for Decentralized Markov SGD](https://mlsanity.com/paper/2605.01701/) (2026)

## Abstract (arXiv)

We consider the consensual distributed optimization problem and propose an asynchronous version of the Alternating Direction Method of Multipliers (ADMM) algorithm to solve it. The `asynchronous' part here refers to the fact that only one node/processor is updated (i.e. performs a minimization step) at each iteration of the algorithm. The selection of the node to be updated is decided by simulating a Markov chain. The proposed algorithm is shown to have a linear convergence property in expectation for the class of functions which are strongly convex and continuously differentiable.