# A Distributed Stochastic Gradient Tracking Method

arXiv: https://arxiv.org/abs/1803.07741 · HTML: https://mlsanity.com/paper/1803.07741/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2018.

## Built on by (most cited first, 3 of 3)

- [Decentralized Gradient Tracking with Local Steps](https://mlsanity.com/paper/2301.01313/) (2023)
- [Distributed Online Non-convex Optimization with Composite Regret](https://mlsanity.com/paper/2209.10105/) (2022)
- [Distributed gradient methods under heavy-tailed communication noise](https://mlsanity.com/paper/2505.24464/) (2025)

## Abstract (arXiv)

In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method. We show that, in expectation, the iterates generated by each agent are attracted to a neighborhood of the optimal solution, where they accumulate exponentially fast (under a constant step size choice). More importantly, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size, which is a comparable performance to a centralized stochastic gradient algorithm. Numerical examples further demonstrate the effectiveness of the method.