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Despite the strong theoretical guarantees that variance-reduced finite-sum optimization algorithms enjoy, their applicability remains limited to cases where the memory overhead they introduce (SAG/SAGA), or the periodic full gradient…

Optimization and Control · Mathematics 2021-03-24 Ayoub El Hanchi , David A. Stephens

We provide the first theoretical analysis on the convergence rate of the asynchronous stochastic variance reduced gradient (SVRG) descent algorithm on non-convex optimization. Recent studies have shown that the asynchronous stochastic…

Machine Learning · Computer Science 2016-12-21 Zhouyuan Huo , Heng Huang

In this paper, we introduce an unbiased gradient simulation algorithms for solving convex optimization problem with stochastic function compositions. We show that the unbiased gradient generated from the algorithm has finite variance and…

Optimization and Control · Mathematics 2017-11-22 Jose Blanchet , Donald Goldfarb , Garud Iyengar , Fengpei Li , Chaoxu Zhou

In this work we introduce a new optimisation method called SAGA in the spirit of SAG, SDCA, MISO and SVRG, a set of recently proposed incremental gradient algorithms with fast linear convergence rates. SAGA improves on the theory behind SAG…

Machine Learning · Computer Science 2014-12-17 Aaron Defazio , Francis Bach , Simon Lacoste-Julien

In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in…

Machine Learning · Statistics 2014-08-14 Taiji Suzuki

In this paper we apply the stochastic variance reduced gradient (SVRG) method, which is a popular variance reduction method in optimization for accelerating the stochastic gradient method, to solve large scale linear ill-posed systems in…

Numerical Analysis · Mathematics 2024-03-20 Qinian Jin , Liuhong Chen

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…

Statistics Theory · Mathematics 2022-01-12 Antoine Godichon-Baggioni

Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…

Machine Learning · Computer Science 2011-11-04 Sangkyun Lee , Stephen J. Wright

Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with…

Optimization and Control · Mathematics 2021-01-01 Lihua Lei , Michael I. Jordan

Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror…

Optimization and Control · Mathematics 2021-12-20 Yiyuan She , Zhifeng Wang , Jiuwu Jin

Sparse linear regression (SLR) is a well-studied problem in statistics where one is given a design matrix $X\in\mathbb{R}^{m\times n}$ and a response vector $y=X\theta^*+w$ for a $k$-sparse vector $\theta^*$ (that is, $\|\theta^*\|_0\leq…

Machine Learning · Computer Science 2025-02-06 Aparna Gupte , Neekon Vafa , Vinod Vaikuntanathan

We study the last-iterate convergence of variance reduction methods for extragradient (EG) algorithms for a class of variational inequalities satisfying error-bound conditions. Previously, last-iterate linear convergence was only known…

Optimization and Control · Mathematics 2024-01-02 Tianlong Nan , Yuan Gao , Christian Kroer

We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…

Optimization and Control · Mathematics 2020-02-28 Derek Driggs , Jingwei Liang , Carola-Bibiane Schönlieb

We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on…

Machine Learning · Computer Science 2013-06-11 Francis Bach , Eric Moulines

Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to…

Machine Learning · Computer Science 2016-10-18 Ohad Shamir

Stochastic gradient method (SGM) has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions. Most existing works on SGMs assume that the underlying problem is unconstrained or…

Optimization and Control · Mathematics 2019-06-19 Yangyang Xu

Convex regression (CR) is the problem of fitting a convex function to a finite number of noisy observations of an underlying convex function. CR is important in many domains and one of its workhorses is the non-parametric least square…

Information Theory · Computer Science 2020-03-03 Andrea Simonetto

Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for…

Machine Learning · Statistics 2017-11-16 Alberto Bietti , Julien Mairal

Many recent applications in machine learning and data fitting call for the algorithmic solution of structured smooth convex optimization problems. Although the gradient descent method is a natural choice for this task, it requires exact…

Optimization and Control · Mathematics 2013-09-03 Anthony Man-Cho So

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…

Machine Learning · Computer Science 2020-10-20 Dongruo Zhou , Pan Xu , Quanquan Gu