# Distributed Stochastic Approximation: Weak Convergence and Network Design

arXiv: https://arxiv.org/abs/1412.3158 · HTML: https://mlsanity.com/paper/1412.3158/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2014.

## Built on by (most cited first, 2 of 2)

- [Finite-Time Error Bounds for Distributed Linear Stochastic Approximation](https://mlsanity.com/paper/2111.12665/) (2021)
- [Core-Halo Decomposition: Decentralizing Large-Scale Fixed-Point Problems](https://mlsanity.com/paper/2605.08681/) (2026)

## Abstract (arXiv)

This paper studies distributed stochastic approximation algorithms based on broadcast gossip on communication networks represented by digraphs. Weak convergence of these algorithms is proved, and an associated ordinary differential equation (ODE) is formulated connecting convergence points with local objective functions and network properties. Using these results, a methodology is proposed for network design, aimed at achieving the desired asymptotic behavior at consensus. Convergence rate of the algorithm is also analyzed and further improved using an attached stochastic differential equation. Simulation results illustrate the theoretical concepts.