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We study a stochastic anchored gradient scheme, namely HalpernSGD, which combines the classical Halpern iteration for finding a minimizer of a convex and $L$-smooth objective function with a stochastic {first-order} oracle. The algorithm is…

Optimization and Control · Mathematics 2026-03-24 Vittorio Colao , Katherine Rossella Foglia

Extragradient method (EG) (Korpelevich, 1976) is one of the most popular methods for solving saddle point and variational inequalities problems (VIP). Despite its long history and significant attention in the optimization community, there…

Optimization and Control · Mathematics 2022-02-23 Eduard Gorbunov , Nicolas Loizou , Gauthier Gidel

Adaptive gradient methods, such as AdaGrad, are among the most successful optimization algorithms for neural network training. While these methods are known to achieve better dimensional dependence than stochastic gradient descent (SGD) for…

Optimization and Control · Mathematics 2025-06-09 Ruichen Jiang , Devyani Maladkar , Aryan Mokhtari

We study the asynchronous stochastic gradient descent algorithm for distributed training over $n$ workers which have varying computation and communication frequency over time. In this algorithm, workers compute stochastic gradients in…

Machine Learning · Computer Science 2022-06-17 Anastasia Koloskova , Sebastian U. Stich , Martin Jaggi

In this work we consider the stochastic minimization of nonsmooth convex loss functions, a central problem in machine learning. We propose a novel algorithm called Accelerated Nonsmooth Stochastic Gradient Descent (ANSGD), which exploits…

Machine Learning · Computer Science 2012-10-02 Hua Ouyang , Alexander Gray

In the vanishing learning rate regime, stochastic gradient descent (SGD) is now relatively well understood. In this work, we propose to study the basic properties of SGD and its variants in the non-vanishing learning rate regime. The focus…

Machine Learning · Statistics 2021-06-14 Kangqiao Liu , Liu Ziyin , Masahito Ueda

We study stochastic gradient descent (SGD) with gradient clipping on convex functions under a generalized smoothness assumption called $(L_0,L_1)$-smoothness. Using gradient clipping, we establish a high probability convergence rate that…

Optimization and Control · Mathematics 2025-06-04 Ofir Gaash , Kfir Yehuda Levy , Yair Carmon

We obtain an improved finite-sample guarantee on the linear convergence of stochastic gradient descent for smooth and strongly convex objectives, improving from a quadratic dependence on the conditioning $(L/\mu)^2$ (where $L$ is a bound on…

Numerical Analysis · Mathematics 2015-01-19 Deanna Needell , Nathan Srebro , Rachel Ward

Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine learning. The noise encountered in these applications is different from that in many theoretical analyses of stochastic gradient algorithms. In this…

Machine Learning · Statistics 2021-09-16 Stephan Wojtowytsch

Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…

Optimization and Control · Mathematics 2024-03-08 David Newton , Raghu Bollapragada , Raghu Pasupathy , Nung Kwan Yip

This work investigates the performance of the final iterate produced by stochastic gradient descent (SGD) under temporally dependent data. We consider two complementary sources of dependence: $(i)$ martingale-type dependence in both the…

Statistics Theory · Mathematics 2026-01-06 Yinan Shen , Yichen Zhang , Wen-Xin Zhou

Stochastic gradient descent (SGD) and its variants are widely used and highly effective optimization methods in machine learning, especially for neural network training. By using a single datum or a small subset of the data, selected…

Numerical Analysis · Mathematics 2026-01-21 Bangti Jin , Zeljko Kereta , Yuxin Xia

Stochastic Gradient Descent or SGD is the most popular optimization algorithm for large-scale problems. SGD estimates the gradient by uniform sampling with sample size one. There have been several other works that suggest faster epoch-wise…

Machine Learning · Computer Science 2019-11-01 Beidi Chen , Yingchen Xu , Anshumali Shrivastava

Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures. For computational reasons, the…

Machine Learning · Computer Science 2024-03-19 Eloi Tanguy

We identify and analyze a fundamental limitation of the classical projected subgradient method in nonsmooth convex optimization: the inevitable failure caused by the absence of valid subgradients at boundary points. We show that, under…

Optimization and Control · Mathematics 2026-02-17 Zhihan Zhu , Yanhao Zhang , Yong Xia

The article considers minimization of the expectation of convex function. Problems of this type often arise in machine learning and a number of other applications. In practice, stochastic gradient descent (SGD) and similar procedures are…

Optimization and Control · Mathematics 2020-11-10 Egor Gladin , Karina Zaynullina

Stochastic gradient descent (SGD) is almost ubiquitously used for training non-convex optimization tasks. Recently, a hypothesis proposed by Keskar et al. [2017] that large batch methods tend to converge to sharp minimizers has received…

Machine Learning · Statistics 2018-12-04 Xiaowu Dai , Yuhua Zhu

Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…

Machine Learning · Computer Science 2024-09-17 Haihan Zhang , Yuanshi Liu , Qianwen Chen , Cong Fang

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

There has been a growing effort in studying the distributed optimization problem over a network. The objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. Literature…

Optimization and Control · Mathematics 2017-05-02 Guannan Qu , Na Li