# An Accelerated Distributed Stochastic Gradient Method with Momentum

arXiv: https://arxiv.org/abs/2402.09714 · HTML: https://mlsanity.com/paper/2402.09714/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2024.

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

- [OledFL: Unleashing the Potential of Decentralized Federated Learning via Opposite Lookahead Enhancement](https://mlsanity.com/paper/2410.06482/) (2024)
- [A Bias-Correction Decentralized Stochastic Gradient Algorithm with Momentum Acceleration](https://mlsanity.com/paper/2501.19082/) (2025)
- [Decentralized Nonconvex Composite Federated Learning with Gradient Tracking and Momentum](https://mlsanity.com/paper/2504.12742/) (2025)

## Abstract (arXiv)

In this paper, we introduce an accelerated distributed stochastic gradient method with momentum for solving the distributed optimization problem, where a group of n agents collaboratively minimize the average of the local objective functions over a connected network. The method, termed ``Distributed Stochastic Momentum Tracking (DSMT)'', is a single-loop algorithm that utilizes the momentum tracking technique as well as the Loopless Chebyshev Acceleration (LCA) method. We show that DSMT can asymptotically achieve comparable convergence rates as centralized stochastic gradient descent (SGD) method under a general variance condition regarding the stochastic gradients. Moreover, the number of iterations (transient times) required for DSMT to achieve such rates behaves as O(n5/3/(1-λ)) for minimizing general smooth objective functions, and O(√n/(1-λ)) under the Polyak-Lojasiewicz (PL) condition. Here, the term 1-λ denotes the spectral gap of the mixing matrix related to the underlying network topology. Notably, the obtained results do not rely on multiple inter-node communications or stochastic gradient accumulation per iteration, and the transient times are the shortest under the setting to the best of our knowledge.