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Decentralized stochastic optimization has emerged as a fundamental paradigm for large-scale machine learning. However, practical implementations often rely on biased gradient estimators arising from communication compression or inexact…

Optimization and Control · Mathematics 2026-04-10 Qing Xu , Yiwei Liao , Wenqi Fan , Xingxing You , Songyi Dian

The convergence of stochastic gradient descent is highly dependent on the step-size, especially on non-convex problems such as neural network training. Step decay step-size schedules (constant and then cut) are widely used in practice…

Optimization and Control · Mathematics 2021-02-19 Xiaoyu Wang , Sindri Magnússon , Mikael Johansson

Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value $c >0$. It is widely used for example for stabilizing the training of deep learning…

Machine Learning · Computer Science 2023-11-10 Anastasia Koloskova , Hadrien Hendrikx , Sebastian U. Stich

We analyze the convergence of decentralized consensus algorithm with delayed gradient information across the network. The nodes in the network privately hold parts of the objective function and collaboratively solve for the consensus…

Optimization and Control · Mathematics 2018-01-17 Benjamin Sirb , Xiaojing Ye

This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…

Optimization and Control · Mathematics 2025-05-13 Naum Dimitrieski , Jing Cao , Christian Ebenbauer

We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony…

Optimization and Control · Mathematics 2023-04-04 Hamid Reza Feyzmahdavian , Mikael Johansson

The existing analysis of asynchronous stochastic gradient descent (SGD) degrades dramatically when any delay is large, giving the impression that performance depends primarily on the delay. On the contrary, we prove much better guarantees…

Optimization and Control · Mathematics 2023-04-21 Konstantin Mishchenko , Francis Bach , Mathieu Even , Blake Woodworth

Stochastic gradient descent (SGD) with mini-batching is a standard tool in large-scale optimization, yet its theoretical properties under heavy-tailed gradient noise remain largely unexplored. In this paper we study SGD with increasing…

Probability · Mathematics 2026-05-11 Bartosz Glowacki , Rafal Kulik , Philippe Soulier

When training neural networks with low-precision computation, rounding errors often cause stagnation or are detrimental to the convergence of the optimizers; in this paper we study the influence of rounding errors on the convergence of the…

Machine Learning · Statistics 2025-01-22 Lu Xia , Michiel E. Hochstenbach , Stefano Massei

In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to…

Machine Learning · Computer Science 2022-10-11 Vivak Patel , Shushu Zhang , Bowen Tian

We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…

Optimization and Control · Mathematics 2019-04-30 David Kozak , Stephen Becker , Alireza Doostan , Luis Tenorio

We analyze the complexity of biased stochastic gradient methods (SGD), where individual updates are corrupted by deterministic, i.e. biased error terms. We derive convergence results for smooth (non-convex) functions and give improved rates…

Machine Learning · Computer Science 2021-05-11 Ahmad Ajalloeian , Sebastian U. Stich

This paper theoretically reanalyzes the convergence of the mini-batch stochastic gradient descent (SGD) for a structured minimization problem involving a finite-sum function with its gradient being stochastically approximated, and an…

Optimization and Control · Mathematics 2026-04-07 Runze Li , Jintao Xu , Wenxun Xing

The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention…

Numerical Analysis · Mathematics 2020-10-05 Arnulf Jentzen , Philippe von Wurstemberger

Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…

Optimization and Control · Mathematics 2025-03-11 Azar Louzi

In the past several years, the last-iterate convergence of the Stochastic Gradient Descent (SGD) algorithm has triggered people's interest due to its good performance in practice but lack of theoretical understanding. For Lipschitz convex…

Machine Learning · Computer Science 2026-03-20 Zijian Liu , Zhengyuan Zhou

Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-06-25 Dan Alistarh , Christopher De Sa , Nikola Konstantinov

Low-precision training has become crucial for reducing the computational and memory costs of large-scale deep learning. However, quantizing gradients introduces magnitude shrinkage, which can change how stochastic gradient descent (SGD)…

Machine Learning · Computer Science 2026-01-09 Vincent-Daniel Yun

Stochastic gradient optimization is the dominant learning paradigm for a variety of scenarios, from classical supervised learning to modern self-supervised learning. We consider stochastic gradient algorithms for learning problems whose…

Machine Learning · Statistics 2025-08-29 Facheng Yu , Ronak Mehta , Alex Luedtke , Zaid Harchaoui

We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…

Optimization and Control · Mathematics 2024-07-08 David Kozak , Stephen Becker , Alireza Doostan , Luis Tenorio