# Asynchronous Adaptation and Learning over Networks --- Part I: Modeling and Stability Analysis

arXiv: https://arxiv.org/abs/1312.5434 · HTML: https://mlsanity.com/paper/1312.5434/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2013.

## Built on by (most cited first, 7 of 7)

- [Networked Signal and Information Processing](https://mlsanity.com/paper/2210.13767/) (2022)
- [Self-Regulating Random Walks for Resilient Decentralized Learning on Graphs](https://mlsanity.com/paper/2407.11762/) (2024)
- [Fully Distributed Actor-Critic Architecture for Multitask Deep Reinforcement Learning](https://mlsanity.com/paper/2110.12306/) (2021)
- [Asynchronous Distributed Optimization with Delay-free Parameters](https://mlsanity.com/paper/2312.06508/) (2023)
- [Asynchronous Diffusion Learning with Agent Subsampling and Local Updates](https://mlsanity.com/paper/2402.05529/) (2024)
- [Diffusion Learning with Partial Agent Participation and Local Updates](https://mlsanity.com/paper/2505.11307/) (2025)
- [Decentralized Learning via Random Walk with Jumps](https://mlsanity.com/paper/2604.12260/) (2026)

## Abstract (arXiv)

In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We examine asynchronous networks that are subject to fairly general sources of uncertainties, such as changing topologies, random link failures, random data arrival times, and agents turning on and off randomly. Under this model, agents in the network may stop updating their solutions or may stop sending or receiving information in a random manner and without coordination with other agents. We establish in Part I conditions on the first and second-order moments of the relevant parameter distributions to ensure mean-square stable behavior. We derive in Part II expressions that reveal how the various parameters of the asynchronous behavior influence network performance. We compare in Part III the performance of asynchronous networks to the performance of both centralized solutions and synchronous networks. One notable conclusion is that the mean-square-error performance of asynchronous networks shows a degradation only of the order of O(nu), where nu is a small step-size parameter, while the convergence rate remains largely unaltered. The results provide a solid justification for the remarkable resilience of cooperative networks in the face of random failures at multiple levels: agents, links, data arrivals, and topology.