English
Related papers

Related papers: Bayesian interpretation of SGD as Ito process

200 papers

We analyze the dynamics of streaming stochastic gradient descent (SGD) in the high-dimensional limit when applied to generalized linear models and multi-index models (e.g. logistic regression, phase retrieval) with general data-covariance.…

Optimization and Control · Mathematics 2023-08-21 Elizabeth Collins-Woodfin , Courtney Paquette , Elliot Paquette , Inbar Seroussi

Stochastic differential equations (SDE) are widely used in modeling stochastic dynamics in literature. However, SDE alone is not enough to determine a unique process. A specified interpretation for stochastic integration is needed.…

Mathematical Physics · Physics 2012-10-18 Jianghong Shi , Tianqi Chen , Ruoshi Yuan , Bo Yuan , Ping Ao

The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…

Optimization and Control · Mathematics 2025-11-21 Fabio Nobile , Matteo Raviola , Nathan Schaeffer

Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…

Machine Learning · Computer Science 2016-01-14 Yadong Mu , Wei Liu , Wei Fan

We present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic quadratic constraints to formulate a small linear matrix…

Optimization and Control · Mathematics 2020-03-31 Bin Hu , Peter Seiler , Laurent Lessard

Stochastic gradient descent (SGD) and its variants are the main workhorses for solving large-scale optimization problems with nonconvex objective functions. Although the convergence of SGDs in the (strongly) convex case is well-understood,…

Machine Learning · Computer Science 2023-10-20 Aritra Dutta , El Houcine Bergou , Soumia Boucherouite , Nicklas Werge , Melih Kandemir , Xin Li

Stochastic Gradient Descent (SGD) is one of the most popular algorithms in statistical and machine learning due to its computational and memory efficiency. Various averaging schemes have been proposed to accelerate the convergence of SGD in…

Machine Learning · Statistics 2025-04-08 Ziyang Wei , Wanrong Zhu , Wei Biao Wu

Stochastic Gradient Descent (SGD) is a widely deployed optimization procedure throughout data-driven and simulation-driven disciplines, which has drawn a substantial interest in understanding its global behavior across a broad class of…

Optimization and Control · Mathematics 2021-04-02 Vivak Patel , Shushu Zhang

Inverse problems in scientific computing often require optimization over infinite-dimensional Hilbert spaces. A commonly used solver in such settings is stochastic gradient descent (SGD), where gradients are approximated using randomly…

Optimization and Control · Mathematics 2026-04-14 Sandra Cerrai , Qin Li , Anjali Nair , Jaeyoung Yoon

Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…

Machine Learning · Computer Science 2024-02-13 Anuraganand Sharma

Stochastic gradient descent (SGD) is the main algorithm behind a large body of work in machine learning. In many cases, constraints are enforced via projections, leading to projected stochastic gradient algorithms. In recent years, a large…

Optimization and Control · Mathematics 2025-10-06 Yuping Zheng , Andrew Lamperski

We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more information about the ASGD dynamics and elucidates the…

Machine Learning · Statistics 2020-03-04 Jing An , Jianfeng Lu , Lexing Ying

Most results on Stochastic Gradient Descent (SGD) in the convex and smooth setting are presented under the form of bounds on the ergodic function value gap. It is an open question whether bounds can be derived directly on the last iterate…

Optimization and Control · Mathematics 2025-07-21 Guillaume Garrigos , Daniel Cortild , Lucas Ketels , Juan Peypouquet

Stochastic Gradient Langevin Dynamics (SGLD) ensures strong guarantees with regards to convergence in measure for sampling log-concave posterior distributions by adding noise to stochastic gradient iterates. Given the size of many practical…

Machine Learning · Computer Science 2020-06-15 Vyacheslav Kungurtsev , Bapi Chatterjee , Dan Alistarh

We study stochastic gradient descent (SGD) for composite optimization problems with $N$ sequential operators subject to perturbations in both the forward and backward passes. Unlike classical analyses that treat gradient noise as additive…

Optimization and Control · Mathematics 2026-02-25 Boao Kong , Hengrui Zhang , Kun Yuan

We study the Stochastic Gradient Langevin Dynamics (SGLD) algorithm for non-convex optimization. The algorithm performs stochastic gradient descent, where in each step it injects appropriately scaled Gaussian noise to the update. We analyze…

Machine Learning · Computer Science 2018-04-10 Yuchen Zhang , Percy Liang , Moses Charikar

In this paper we analyze the behaviour of the stochastic gradient descent (SGD), a widely used method in supervised learning for optimizing neural network weights via a minimization of non-convex loss functions. Since the pioneering work of…

Machine Learning · Computer Science 2025-05-13 Davide Barbieri , Matteo Bonforte , Peio Ibarrondo

Stochastic Gradient Descent (SGD) methods see many uses in optimization problems. Modifications to the algorithm, such as momentum-based SGD methods have been known to produce better results in certain cases. Much of this, however, is due…

Machine Learning · Computer Science 2025-04-22 Eric Lu

We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of…

Machine Learning · Computer Science 2025-03-06 Tehila Dahan , Kfir Y. Levy

Stochastic gradient descent (SGD) is a pillar of modern machine learning, serving as the go-to optimization algorithm for a diverse array of problems. While the empirical success of SGD is often attributed to its computational efficiency…

Machine Learning · Statistics 2022-06-16 Courtney Paquette , Elliot Paquette , Ben Adlam , Jeffrey Pennington