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We prove convergence of a single time-scale stochastic subgradient method with subgradient averaging for constrained problems with a nonsmooth and nonconvex objective function having the property of generalized differentiability. As a tool…

Optimization and Control · Mathematics 2019-12-17 Andrzej Ruszczynski

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…

Optimization and Control · Mathematics 2019-02-06 Yi Xu , Zhuoning Yuan , Sen Yang , Rong Jin , Tianbao Yang

The stochastic subgradient method is a widely-used algorithm for solving large-scale optimization problems arising in machine learning. Often these problems are neither smooth nor convex. Recently, Davis et al. [1-2] characterized the…

Optimization and Control · Mathematics 2021-02-25 Shixiang Chen , Alfredo Garcia , Shahin Shahrampour

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…

Machine Learning · Statistics 2015-11-13 Mengdi Wang , Yichen Chen , Jialin Liu , Yuantao Gu

In this paper, we present a stochastic gradient algorithm for minimizing a smooth objective function that is an expectation over noisy cost samples, and only the latter are observed for any given parameter. Our algorithm employs a gradient…

Optimization and Control · Mathematics 2023-07-03 Akash Mondal , Prashanth L. A. , Shalabh Bhatnagar

We propose a new stochastic first-order algorithmic framework to solve stochastic composite nonconvex optimization problems that covers both finite-sum and expectation settings. Our algorithms rely on the SARAH estimator introduced in…

Optimization and Control · Mathematics 2019-04-01 Nhan H. Pham , Lam M. Nguyen , Dzung T. Phan , Quoc Tran-Dinh

Stochastic optimization lies at the core of most statistical learning models. The recent great development of stochastic algorithmic tools focused significantly onto proximal gradient iterations, in order to find an efficient approach for…

Machine Learning · Computer Science 2020-03-31 Andrei Patrascu , Ciprian Paduraru , Paul Irofti

We show that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal (even to constant factors) convergence rates for the solution of convex optimization problems under nearly the same conditions required for…

Optimization and Control · Mathematics 2015-08-05 John C. Duchi , Sorathan Chaturapruek , Christopher Ré

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

Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…

Optimization and Control · Mathematics 2021-06-18 Caroline Geiersbach , Winnifried Wollner

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

We study the non-smooth optimization problems in machine learning, where both the loss function and the regularizer are non-smooth functions. Previous studies on efficient empirical loss minimization assume either a smooth loss function or…

Machine Learning · Computer Science 2013-07-29 Tianbao Yang , Mehrdad Mahdavi , Rong Jin , Shenghuo Zhu

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

Optimization and Control · Mathematics 2020-01-22 Mohammad S. Alkousa

Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are…

Optimization and Control · Mathematics 2024-09-02 Eduard Gorbunov , Marina Danilova , Innokentiy Shibaev , Pavel Dvurechensky , Alexander Gasnikov

We develop a class of algorithms, as variants of the stochastically controlled stochastic gradient (SCSG) methods (Lei and Jordan, 2016), for the smooth non-convex finite-sum optimization problem. Assuming the smoothness of each component,…

Optimization and Control · Mathematics 2019-05-17 Lihua Lei , Cheng Ju , Jianbo Chen , Michael I. Jordan

This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…

Optimization and Control · Mathematics 2025-08-05 Chenglong Bao , Liang Chen , Weizhi Shao

Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…

Machine Learning · Computer Science 2013-01-01 Ohad Shamir , Tong Zhang

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

Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimization methods. However, these procedures cannot be used in…

Optimization and Control · Mathematics 2025-07-01 Marco Rando , Cheik Traoré , Cesare Molinari , Lorenzo Rosasco , Silvia Villa

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…

Optimization and Control · Mathematics 2022-03-02 Boris S. Mordukhovich , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang