# Robust Distributed Accelerated Stochastic Gradient Methods for Multi-Agent Networks

arXiv: https://arxiv.org/abs/1910.08701 · HTML: https://mlsanity.com/paper/1910.08701/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2019.

## Built on by (most cited first, 9 of 9)

- [Moshpit SGD: Communication-Efficient Decentralized Training on Heterogeneous Unreliable Devices](https://mlsanity.com/paper/2103.03239/) (2021)
- [Accelerated Gradient Tracking over Time-varying Graphs for Decentralized Optimization](https://mlsanity.com/paper/2104.02596/) (2021)
- [Heavy-Tail Phenomenon in Decentralized SGD](https://mlsanity.com/paper/2205.06689/) (2022)
- [Uniform-in-Time Wasserstein Stability Bounds for (Noisy) Stochastic Gradient Descent](https://mlsanity.com/paper/2305.12056/) (2023)
- [DIGing--SGLD: Decentralized and Scalable Langevin Sampling over Time--Varying Networks](https://mlsanity.com/paper/2511.12836/) (2025)
- [Provably Accelerated Decentralized Gradient Method Over Unbalanced Directed Graphs](https://mlsanity.com/paper/2107.12065/) (2021)
- [Accelerated Gradient Methods with Biased Gradient Estimates: Risk Sensitivity, High-Probability Guarantees, and Large Deviation Bounds](https://mlsanity.com/paper/2509.13628/) (2025)
- [Accelerated Decentralized Stochastic Gradient Descent for Strongly Convex Optimization](https://mlsanity.com/paper/2606.07496/) (2026)
- [Accelerating Distributed Optimization: A Primal-Dual Perspective on Local Steps](https://mlsanity.com/paper/2407.02689/) (2024)

## Abstract (arXiv)

We study distributed stochastic gradient (D-SG) method and its accelerated variant (D-ASG) for solving decentralized strongly convex stochastic optimization problems where the objective function is distributed over several computational units, lying on a fixed but arbitrary connected communication graph, subject to local communication constraints where noisy estimates of the gradients are available. We develop a framework which allows to choose the stepsize and the momentum parameters of these algorithms in a way to optimize performance by systematically trading off the bias, variance, robustness to gradient noise and dependence to network effects. When gradients do not contain noise, we also prove that distributed accelerated methods can achieve acceleration, requiring O(kappa log(1/varepsilon)) gradient evaluations and O(kappa log(1/varepsilon)) communications to converge to the same fixed point with the non-accelerated variant where kappa is the condition number and varepsilon is the target accuracy. To our knowledge, this is the first acceleration result where the iteration complexity scales with the square root of the condition number in the context of primal distributed inexact first-order methods. For quadratic functions, we also provide finer performance bounds that are tight with respect to bias and variance terms. Finally, we study a multistage version of D-ASG with parameters carefully varied over stages to ensure exact O(-k/√kappa) linear decay in the bias term as well as optimal O(σ2/k) in the variance term. We illustrate through numerical experiments that our approach results in practical algorithms that are robust to gradient noise and that can outperform existing methods.