# Distributed Coupled Multi-Agent Stochastic Optimization

arXiv: https://arxiv.org/abs/1712.08817 · HTML: https://mlsanity.com/paper/1712.08817/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2017.

## Built on by (most cited first, 6 of 6)

- [Quantization for decentralized learning under subspace constraints](https://mlsanity.com/paper/2209.07821/) (2022)
- [Differential error feedback for communication-efficient decentralized learning](https://mlsanity.com/paper/2406.18418/) (2024)
- [Distributed Fractional Bayesian Learning for Adaptive Optimization](https://mlsanity.com/paper/2404.11354/) (2024)
- [Rate Analysis of Coupled Distributed Stochastic Approximation for Misspecified Optimization](https://mlsanity.com/paper/2404.13669/) (2024)
- [Estimation Network Design framework for efficient distributed optimization](https://mlsanity.com/paper/2404.15273/) (2024)
- [A non-smooth regularization framework for learning over multitask graphs](https://mlsanity.com/paper/2509.17728/) (2025)

## Abstract (arXiv)

This work develops effective distributed strategies for the solution of constrained multi-agent stochastic optimization problems with coupled parameters across the agents. In this formulation, each agent is influenced by only a subset of the entries of a global parameter vector or model, and is subject to convex constraints that are only known locally. Problems of this type arise in several applications, most notably in disease propagation models, minimum-cost flow problems, distributed control formulations, and distributed power system monitoring. This work focuses on stochastic settings, where a stochastic risk function is associated with each agent and the objective is to seek the minimizer of the aggregate sum of all risks subject to a set of constraints. Agents are not aware of the statistical distribution of the data and, therefore, can only rely on stochastic approximations in their learning strategies. We derive an effective distributed learning strategy that is able to track drifts in the underlying parameter model. A detailed performance and stability analysis is carried out showing that the resulting coupled diffusion strategy converges at a linear rate to an O(μ)-neighborhood of the true penalized optimizer.