English
Related papers

Related papers: Non-Convex Optimization via Non-Reversible Stochas…

200 papers

Stochastic gradient Langevin dynamics (SGLD) is a fundamental algorithm in stochastic optimization. Recent work by Zhang et al. [2017] presents an analysis for the hitting time of SGLD for the first and second order stationary points. The…

Machine Learning · Statistics 2020-03-17 Xi Chen , Simon S. Du , Xin T. Tong

The stochastic gradient (SG) method can minimize an objective function composed of a large number of differentiable functions, or solve a stochastic optimization problem, to a moderate accuracy. The block coordinate descent/update (BCD)…

Optimization and Control · Mathematics 2015-11-23 Yangyang Xu , Wotao Yin

We consider a class of stochastic smooth convex optimization problems under rather general assumptions on the noise in the stochastic gradient observation. As opposed to the classical problem setting in which the variance of noise is…

Optimization and Control · Mathematics 2024-08-23 Sasila Ilandarideva , Anatoli Juditsky , Guanghui Lan , Tianjiao Li

We propose a new stochastic optimization framework for empirical risk minimization problems such as those that arise in machine learning. The traditional approaches, such as (mini-batch) stochastic gradient descent (SGD), utilize an…

Machine Learning · Statistics 2020-02-04 Kenji Kawaguchi , Haihao Lu

Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…

Optimization and Control · Mathematics 2026-03-02 Zimeng Wang , Alp Yurtsever

In this paper, we study decentralized online stochastic non-convex optimization over a network of nodes. Integrating a technique called gradient tracking in decentralized stochastic gradient descent, we show that the resulting algorithm,…

Optimization and Control · Mathematics 2021-04-21 Ran Xin , Usman A. Khan , Soummya Kar

This paper considers the generalization performance of differentially private convex learning. We demonstrate that the convergence analysis of Langevin algorithms can be used to obtain new generalization bounds with differential privacy…

Machine Learning · Computer Science 2022-06-07 Yi-An Ma , Teodor Vanislavov Marinov , Tong Zhang

Sampling from a target distribution is a fundamental problem. Traditional Markov chain Monte Carlo (MCMC) algorithms, such as the unadjusted Langevin algorithm (ULA), derived from the overdamped Langevin dynamics, have been extensively…

Optimization and Control · Mathematics 2024-10-29 Xinzhe Zuo , Stanley Osher , Wuchen Li

Multiview representation learning is very popular for latent factor analysis. It naturally arises in many data analysis, machine learning, and information retrieval applications to model dependent structures among multiple data sources. For…

Machine Learning · Computer Science 2019-09-17 Zhehui Chen , Lin F. Yang , Chris J. Li , Tuo Zhao

Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm…

Probability · Mathematics 2019-06-18 Justin Sirignano , Konstantinos Spiliopoulos

We propose a generalized Langevin dynamics (GLD) technique to construct non-Markovian particle-based coarse-grained models from fine-grained reference simulations and to efficiently integrate them. The proposed GLD model has the form of a…

Soft Condensed Matter · Physics 2018-11-16 Gerhard Jung , Martin Hanke , Friederike Schmid

Stochastic convex optimization is a basic and well studied primitive in machine learning. It is well known that convex and Lipschitz functions can be minimized efficiently using Stochastic Gradient Descent (SGD). The Normalized Gradient…

Machine Learning · Computer Science 2015-10-29 Elad Hazan , Kfir Y. Levy , Shai Shalev-Shwartz

We study stochastic algorithms for solving nonconvex optimization problems with a convex yet possibly nonsmooth regularizer, which find wide applications in many practical machine learning applications. However, compared to asynchronous…

Machine Learning · Computer Science 2018-09-18 Rui Zhu , Di Niu , Zongpeng Li

In this paper, we show that simple {Stochastic} subGradient Decent methods with multiple Restarting, named {\bf RSGD}, can achieve a \textit{linear convergence rate} for a class of non-smooth and non-strongly convex optimization problems…

Machine Learning · Computer Science 2016-04-01 Tianbao Yang , Qihang Lin

This paper focuses on the distributed optimization of stochastic saddle point problems. The first part of the paper is devoted to lower bounds for the centralized and decentralized distributed methods for smooth (strongly) convex-(strongly)…

Machine Learning · Computer Science 2025-04-28 Aleksandr Beznosikov , Valentin Samokhin , Alexander Gasnikov

Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…

Machine Learning · Computer Science 2024-09-17 Haihan Zhang , Yuanshi Liu , Qianwen Chen , Cong Fang

Distributionally robust optimization (DRO) is a powerful technique to train robust models against data distribution shift. This paper aims to solve regularized nonconvex DRO problems, where the uncertainty set is modeled by a so-called…

Optimization and Control · Mathematics 2025-06-30 Yufeng Yang , Yi Zhou , Zhaosong Lu

We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly…

Optimization and Control · Mathematics 2018-12-04 Zhize Li , Jian Li

Various gradient compression schemes have been proposed to mitigate the communication cost in distributed training of large scale machine learning models. Sign-based methods, such as signSGD, have recently been gaining popularity because of…

Optimization and Control · Mathematics 2021-06-25 Mher Safaryan , Peter Richtárik

In this paper, we propose a method of distributed stochastic gradient descent (SGD), with low communication load and computational complexity, and still fast convergence. To reduce the communication load, at each iteration of the algorithm,…

Machine Learning · Computer Science 2020-03-30 Naeimeh Omidvar , Mohammad Ali Maddah-Ali , Hamed Mahdavi