English
Related papers

Related papers: Efficient Single-Loop Stochastic Algorithms for No…

200 papers

Stochastic gradient descent is the method of choice for large-scale machine learning problems, by virtue of its light complexity per iteration. However, it lags behind its non-stochastic counterparts with respect to the convergence rate,…

Machine Learning · Statistics 2016-03-23 Vatsal Shah , Megasthenis Asteris , Anastasios Kyrillidis , Sujay Sanghavi

In this paper, we study the minimax optimization problem in the smooth and strongly convex-strongly concave setting when we have access to noisy estimates of gradients. In particular, we first analyze the stochastic Gradient Descent Ascent…

Optimization and Control · Mathematics 2020-02-14 Alireza Fallah , Asuman Ozdaglar , Sarath Pattathil

In this paper, we propose a novel sufficient decrease technique for stochastic variance reduced gradient descent methods such as SVRG and SAGA. In order to make sufficient decrease for stochastic optimization, we design a new sufficient…

Machine Learning · Statistics 2018-02-28 Fanhua Shang , Yuanyuan Liu , Kaiwen Zhou , James Cheng , Kelvin K. W. Ng , Yuichi Yoshida

We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…

Optimization and Control · Mathematics 2014-03-20 Lin Xiao , Tong Zhang

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…

Machine Learning · Computer Science 2022-04-19 Gideon Dresdner , Maria-Luiza Vladarean , Gunnar Rätsch , Francesco Locatello , Volkan Cevher , Alp Yurtsever

Stochastic optimization algorithms are widely used for machine learning with large-scale data. However, their convergence often suffers from non-vanishing variance. Variance Reduction (VR) methods, such as SVRG and SARAH, address this issue…

Machine Learning · Computer Science 2026-01-12 Daniil Medyakov , Gleb Molodtsov , Savelii Chezhegov , Alexey Rebrikov , Aleksandr Beznosikov

A popular approach to minimize a finite-sum of convex functions is stochastic gradient descent (SGD) and its variants. Fundamental research questions associated with SGD include: (i) To find a lower bound on the number of times that the…

Optimization and Control · Mathematics 2022-08-16 Nuozhou Wang , Shuzhong Zhang

In this work, we consider strongly convex strongly concave (SCSC) saddle point (SP) problems $\min_{x\in\mathbb{R}^{d_x}}\max_{y\in\mathbb{R}^{d_y}}f(x,y)$ where $f$ is $L$-smooth, $f(.,y)$ is $\mu$-strongly convex for every $y$, and…

Optimization and Control · Mathematics 2022-02-22 Bugra Can , Mert Gurbuzbalaban , Necdet Serhat Aybat

Much recent research effort has been directed to the development of efficient algorithms for solving minimax problems with theoretical convergence guarantees due to the relevance of these problems to a few emergent applications. In this…

Optimization and Control · Mathematics 2023-01-18 Zi Xu , Huiling Zhang , Yang Xu , Guanghui Lan

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a…

Numerical Analysis · Computer Science 2015-09-01 N. Denizcan Vanli , Muhammed O. Sayin , Suleyman S. Kozat

Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…

Optimization and Control · Mathematics 2022-10-06 Melinda Hagedorn , Florian Jarre

Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform…

Machine Learning · Statistics 2015-01-05 Peilin Zhao , Tong Zhang

Variance reduction (VR) methods boost the performance of stochastic gradient descent (SGD) by enabling the use of larger, constant stepsizes and preserving linear convergence rates. However, current variance reduced SGD methods require…

Machine Learning · Computer Science 2017-04-10 Soham De , Gavin Taylor , Tom Goldstein

In the paper, we propose a class of faster adaptive Gradient Descent Ascent (GDA) methods for solving the nonconvex-strongly-concave minimax problems by using the unified adaptive matrices, which include almost all existing coordinate-wise…

Optimization and Control · Mathematics 2023-02-22 Feihu Huang , Xidong Wu , Zhengmian Hu

An increasing number of machine learning problems, such as robust or adversarial variants of existing algorithms, require minimizing a loss function that is itself defined as a maximum. Carrying a loop of stochastic gradient ascent (SGA)…

Machine Learning · Computer Science 2021-11-29 Othmane Sebbouh , Marco Cuturi , Gabriel Peyré

In this work, we investigate the idea of variance reduction by studying its properties with general adaptive mirror descent algorithms in nonsmooth nonconvex finite-sum optimization problems. We propose a simple yet generalized framework…

Machine Learning · Statistics 2022-10-18 Wenjie Li , Zhanyu Wang , Yichen Zhang , Guang Cheng

In this work, we propose and analyze DCA-PAGE, a novel algorithm that integrates the difference-of-convex algorithm (DCA) with the ProbAbilistic Gradient Estimator (PAGE) to solve structured nonsmooth difference-of-convex programs. In the…

Optimization and Control · Mathematics 2025-09-16 Anh Duc Nguyen , Alp Yurtsever , Suvrit Sra , Kim-Chuan Toh

This paper describes a novel algorithmic framework to minimize a finite-sum of functions available over a network of nodes. The proposed framework, that we call~\GTVR, is stochastic and decentralized, and thus is particularly suitable for…

Optimization and Control · Mathematics 2020-12-02 Ran Xin , Usman A. Khan , Soummya Kar

Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…

Optimization and Control · Mathematics 2019-05-15 Michael R. Metel , Akiko Takeda

We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…

Optimization and Control · Mathematics 2012-04-10 John C. Duchi , Peter L. Bartlett , Martin J. Wainwright