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In this paper, we study the stochastic gradient descent (SGD) method for the nonconvex nonsmooth optimization, and propose an accelerated SGD method by combining the variance reduction technique with Nesterov's extrapolation technique.…

Optimization and Control · Mathematics 2019-02-18 Feihu Huang , Songcan Chen

Nonsmooth sparsity constrained optimization encompasses a broad spectrum of applications in machine learning. This problem is generally non-convex and NP-hard. Existing solutions to this problem exhibit several notable limitations,…

Optimization and Control · Mathematics 2023-12-18 Ganzhao Yuan

In the past several years, the last-iterate convergence of the Stochastic Gradient Descent (SGD) algorithm has triggered people's interest due to its good performance in practice but lack of theoretical understanding. For Lipschitz convex…

Machine Learning · Computer Science 2026-03-20 Zijian Liu , Zhengyuan Zhou

Large-scale nonconvex optimization problems are ubiquitous in modern machine learning, and among practitioners interested in solving them, Stochastic Gradient Descent (SGD) reigns supreme. We revisit the analysis of SGD in the nonconvex…

Optimization and Control · Mathematics 2020-07-27 Ahmed Khaled , Peter Richtárik

Stochastic Gradient Descent (SGD) is widely used in machine learning research. Previous convergence analyses of SGD under the vanishing step-size setting typically require Robbins-Monro conditions. However, in practice, a wider variety of…

Machine Learning · Computer Science 2025-04-18 Ruinan Jin , Difei Cheng , Hong Qiao , Xin Shi , Shaodong Liu , Bo Zhang

Stochastic gradient descent (SGD) gives an optimal convergence rate when minimizing convex stochastic objectives $f(x)$. However, in terms of making the gradients small, the original SGD does not give an optimal rate, even when $f(x)$ is…

Machine Learning · Computer Science 2021-07-30 Zeyuan Allen-Zhu

Asynchronous parallel optimization algorithms for solving large-scale machine learning problems have drawn significant attention from academia to industry recently. This paper proposes a novel algorithm, decoupled asynchronous proximal…

Optimization and Control · Mathematics 2016-05-24 Yitan Li , Linli Xu , Xiaowei Zhong , Qing Ling

Here we study non-convex composite optimization: first, a finite-sum of smooth but non-convex functions, and second, a general function that admits a simple proximal mapping. Most research on stochastic methods for composite optimization…

Machine Learning · Statistics 2016-09-13 Xiyu Yu , Dacheng Tao

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

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

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

Optimization and Control · Mathematics 2022-02-16 Meng Li , Paul Grigas , Alper Atamturk

In this paper, we propose a proximal stochasitc gradient algorithm (PSGA) for solving composite optimization problems by incorporating variance reduction techniques and an adaptive step-size strategy. In the PSGA method, the objective…

Optimization and Control · Mathematics 2026-04-06 Changjie Fang , Hao Yang , Shenglan Chen

We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of…

Machine Learning · Computer Science 2025-03-06 Tehila Dahan , Kfir Y. Levy

We propose a sequential quadratic programming (SQP) method that can incorporate adaptive sampling for stochastic nonsmooth nonconvex optimization problems with upper-C^2 objectives. Upper-$\Ctwo$ functions can be viewed as…

Optimization and Control · Mathematics 2023-10-17 J. Wang , I. Aravena , C. G. Petra

The proximal stochastic gradient method (PSGD) is one of the state-of-the-art approaches for stochastic composite-type problems. In contrast to its deterministic counterpart, PSGD has been found to have difficulties with the correct…

Optimization and Control · Mathematics 2026-03-04 Junwen Qiu , Li Jiang , Andre Milzarek

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

The Stochastic Gradient Descent method (SGD) and its stochastic variants have become methods of choice for solving finite-sum optimization problems arising from machine learning and data science thanks to their ability to handle large-scale…

Optimization and Control · Mathematics 2024-03-06 Trang H. Tran , Quoc Tran-Dinh , Lam M. Nguyen

The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…

Optimization and Control · Mathematics 2026-02-24 Zhirayr Tovmasyan , Grigory Malinovsky , Laurent Condat , Peter Richtárik

Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…

Machine Learning · Computer Science 2024-02-13 Anuraganand Sharma

Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are batch methods designed mainly based on the convex optimization, say, the…

Machine Learning · Statistics 2018-02-01 Ke Ma , Jinshan Zeng , Jiechao Xiong , Qianqian Xu , Xiaochun Cao , Wei Liu , Yuan Yao