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Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…

Machine Learning · Statistics 2017-05-10 Yuting Ma , Tian Zheng

We consider stochastic approximation for the least squares regression problem in the non-strongly convex setting. We present the first practical algorithm that achieves the optimal prediction error rates in terms of dependence on the noise…

Machine Learning · Computer Science 2022-03-04 Aditya Varre , Nicolas Flammarion

We study high-probability convergence guarantees of learning on streaming data in the presence of heavy-tailed noise. In the proposed scenario, the model is updated in an online fashion, as new information is observed, without storing any…

Machine Learning · Computer Science 2024-05-02 Aleksandar Armacki , Pranay Sharma , Gauri Joshi , Dragana Bajovic , Dusan Jakovetic , Soummya Kar

In this paper we study the problem of convergence and generalization error bound of stochastic momentum for deep learning from the perspective of regularization. To do so, we first interpret momentum as solving an $\ell_2$-regularized…

Machine Learning · Computer Science 2019-06-04 Ziming Zhang , Wenju Xu , Alan Sullivan

A variant of consensus based distributed gradient descent (\textbf{DGD}) is studied for finite sums of smooth but possibly non-convex functions. In particular, the local gradient term in the fixed step-size iteration of each agent is…

Optimization and Control · Mathematics 2026-05-27 Lei Qin , Michael Cantoni , Ye Pu

Stochastic gradient descent (SGD) is a workhorse algorithm for solving large-scale optimization problems in data science and machine learning. Understanding the convergence of SGD is hence of fundamental importance. In this work we examine…

Numerical Analysis · Mathematics 2024-12-11 Lehan Chen , Yuji Nakatsukasa

In this paper we introduce a unified analysis of a large family of variants of proximal stochastic gradient descent ({\tt SGD}) which so far have required different intuitions, convergence analyses, have different applications, and which…

Optimization and Control · Mathematics 2019-05-28 Eduard Gorbunov , Filip Hanzely , Peter Richtárik

Stochastic Gradient Descent (SGD) is the standard numerical method used to solve the core optimization problem for the vast majority of machine learning (ML) algorithms. In the context of large scale learning, as utilized by many Big Data…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-10-06 Janis Keuper , Franz-Josef Pfreundt

This paper develops asymptotic theory for quantile estimation via stochastic gradient descent (SGD) with a constant learning rate. The quantile loss function is neither smooth nor strongly convex. Beyond conventional perspectives and…

Machine Learning · Statistics 2026-04-06 Ziyang Wei , Jiaqi Li , Likai Chen , Wei Biao Wu

The Stochastic Gradient Descent method (SGD) and its stochastic variants have become methods of choice for solving finite-sum optimization problems arising from machine learning and data science thanks to their ability to handle large-scale…

Optimization and Control · Mathematics 2024-03-06 Trang H. Tran , Quoc Tran-Dinh , Lam M. Nguyen

Stochastic Gradient Descent (SGD) and its variants are the most used algorithms in machine learning applications. In particular, SGD with adaptive learning rates and momentum is the industry standard to train deep networks. Despite the…

Machine Learning · Statistics 2020-07-29 Xiaoyu Li , Francesco Orabona

Stochastic gradient descent (SGD) type optimization schemes are fundamental ingredients in a large number of machine learning based algorithms. In particular, SGD type optimization schemes are frequently employed in applications involving…

Numerical Analysis · Mathematics 2020-07-22 Aritz Bercher , Lukas Gonon , Arnulf Jentzen , Diyora Salimova

The stochastic gradient noise (SGN) is a significant factor in the success of stochastic gradient descent (SGD). Following the central limit theorem, SGN was initially modeled as Gaussian, and lately, it has been suggested that stochastic…

Machine Learning · Computer Science 2023-03-07 Barak Battash , Ofir Lindenbaum

Stochastic Gradient Descent (SGD) plays a central role in modern machine learning. While there is extensive work on providing error upper bound for SGD, not much is known about SGD error lower bound. In this paper, we study the convergence…

Optimization and Control · Mathematics 2019-10-21 Zhiyan Ding , Yiding Chen , Qin Li , Xiaojin Zhu

In recent years, stochastic gradient descent (SGD) methods and randomized linear algebra (RLA) algorithms have been applied to many large-scale problems in machine learning and data analysis. We aim to bridge the gap between these two…

Optimization and Control · Mathematics 2017-07-11 Jiyan Yang , Yin-Lam Chow , Christopher Ré , Michael W. Mahoney

Stochastic Gradient Descent (SGD) based methods have been widely used for training large-scale machine learning models that also generalize well in practice. Several explanations have been offered for this generalization performance, a…

Machine Learning · Computer Science 2021-02-11 Yikai Zhang , Wenjia Zhang , Sammy Bald , Vamsi Pingali , Chao Chen , Mayank Goswami

Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an…

Machine Learning · Statistics 2018-01-23 Stephan Mandt , Matthew D. Hoffman , David M. Blei

It is generally recognized that finite learning rate (LR), in contrast to infinitesimal LR, is important for good generalization in real-life deep nets. Most attempted explanations propose approximating finite-LR SGD with Ito Stochastic…

Machine Learning · Computer Science 2021-06-18 Zhiyuan Li , Sadhika Malladi , Sanjeev Arora

Understanding the implicit bias of Stochastic Gradient Descent (SGD) is one of the key challenges in deep learning, especially for overparametrized models, where the local minimizers of the loss function $L$ can form a manifold.…

Machine Learning · Computer Science 2022-07-29 Zhiyuan Li , Tianhao Wang , Sanjeev Arora

Stochastic gradient descent (SGD) is a ubiquitous algorithm for a variety of machine learning problems. Researchers and industry have developed several techniques to optimize SGD's runtime performance, including asynchronous execution and…

Machine Learning · Computer Science 2015-10-06 Christopher De Sa , Ce Zhang , Kunle Olukotun , Christopher Ré