# Distributed Stochastic Optimization under Heavy-Tailed Noises

arXiv: https://arxiv.org/abs/2312.15847 · HTML: https://mlsanity.com/paper/2312.15847/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Dec 2023.

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

- [Unbiased and Sign Compression in Distributed Learning: Comparing Noise Resilience via SDEs](https://mlsanity.com/paper/2502.17009/) (2025)
- [Optimal Asynchronous Stochastic Nonconvex Optimization under Heavy-Tailed Noise](https://mlsanity.com/paper/2601.19379/) (2026)
- [Gradient Manipulation in Distributed Stochastic Gradient Descent with Strategic Agents: Truthful Incentives with Convergence Guarantees](https://mlsanity.com/paper/2603.27962/) (2026)

## Abstract (arXiv)

This paper studies the distributed optimization problem under the influence of heavy-tailed gradient noises. Here, a heavy-tailed noise means that the noise does not necessarily satisfy the bounded variance assumption. Instead, it satisfies a more general assumption. The commonly-used bounded variance assumption is a special case of the considered noise assumption. A typical example of this kind of noise is a Pareto distribution noise with tail index within (1,2], which has infinite variance. Despite that there has been several distributed optimization algorithms proposed for the heavy-tailed noise scenario, these algorithms need a centralized server in the network which collects the information of all clients. Different from these algorithms, this paper considers that there is no centralized server and the agents can only exchange information with neighbors in a communication graph. A distributed method combining gradient clipping and distributed stochastic subgradient projection is proposed. It is proven that when the gradient descent step-size and the gradient clipping step-size meet certain conditions, the state of each agent converges to the optimal solution of the distributed optimization problem with probability 1. The simulation results validate the algorithm.