English
Related papers

Related papers: Stochastic Subspace Descent

200 papers

Non-convex optimization problems are ubiquitous in machine learning, especially in Deep Learning. While such complex problems can often be successfully optimized in practice by using stochastic gradient descent (SGD), theoretical analysis…

Machine Learning · Computer Science 2022-02-21 Harsh Vardhan , Sebastian U. Stich

In this work, we consider convex optimization problems with smooth objective function and nonsmooth functional constraints. We propose a new stochastic gradient algorithm, called Stochastic Halfspace Approximation Method (SHAM), to solve…

Optimization and Control · Mathematics 2024-12-04 Nitesh Kumar Singh , Ion Necoara

We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster…

Optimization and Control · Mathematics 2020-01-07 Ashia Wilson , Lester Mackey , Andre Wibisono

Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive…

Machine Learning · Statistics 2018-10-02 Qi Deng , Yi Cheng , Guanghui Lan

We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…

Optimization and Control · Mathematics 2026-02-13 Jan Harold Alcantara , Ching-pei Lee

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…

Optimization and Control · Mathematics 2024-02-01 Digvijay Boob , Qi Deng , Guanghui Lan

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…

Optimization and Control · Mathematics 2021-01-26 Junqi Tang , Karen Egiazarian , Mohammad Golbabaee , Mike Davies

This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We…

Optimization and Control · Mathematics 2024-03-05 Antai Xie , Xinlei Yi , Xiaofan Wang , Ming Cao , Xiaoqiang Ren

Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing…

Machine Learning · Computer Science 2019-12-16 Yunwen Lei , Ting Hu , Guiying Li , Ke Tang

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

Machine Learning · Computer Science 2017-06-06 Fanhua Shang , Yuanyuan Liu , James Cheng , Kelvin Kai Wing Ng , Yuichi Yoshida

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…

Machine Learning · Statistics 2015-06-11 Atsushi Nitanda

In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…

Machine Learning · Statistics 2018-12-27 Lam M. Nguyen , Nam H. Nguyen , Dzung T. Phan , Jayant R. Kalagnanam , Katya Scheinberg

In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic…

Optimization and Control · Mathematics 2018-08-23 Deming Yuan , Yiguang Hong , Daniel W. C. Ho , Guoping Jiang

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 considers the analysis of continuous time gradient-based optimization algorithms through the lens of nonlinear contraction theory. It demonstrates that in the case of a time-invariant objective, most elementary results on…

Optimization and Control · Mathematics 2022-12-23 Patrick M. Wensing , Jean-Jacques E. Slotine

Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus…

Machine Learning · Computer Science 2019-12-03 Fanhua Shang , Bingkun Wei , Hongying Liu , Yuanyuan Liu , Jiacheng Zhuo

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

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. This point of view covers the stochastic gradient…

Machine Learning · Statistics 2019-05-08 Andrei Kulunchakov , Julien Mairal

Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…

Optimization and Control · Mathematics 2023-08-15 Da Li , Jingjing Wu , Qingrun Zhang

Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…

Machine Learning · Statistics 2014-11-17 Mengdi Wang , Ethan X. Fang , Han Liu