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The success of modern machine learning is due in part to the adaptive optimization methods that have been developed to deal with the difficulties of training large models over complex datasets. One such method is gradient clipping: a…

Machine Learning · Statistics 2024-10-08 Noah Marshall , Ke Liang Xiao , Atish Agarwala , Elliot Paquette

Heavy-tailed noise has attracted growing attention in nonconvex stochastic optimization, as numerous empirical studies suggest it offers a more realistic assumption than standard bounded variance assumption. In this work, we investigate…

Machine Learning · Computer Science 2025-11-07 Xinwen Zhang , Hongchang Gao

We analyze the variance of stochastic gradients along negative curvature directions in certain non-convex machine learning models and show that stochastic gradients exhibit a strong component along these directions. Furthermore, we show…

Machine Learning · Computer Science 2018-09-18 Hadi Daneshmand , Jonas Kohler , Aurelien Lucchi , Thomas Hofmann

Differentially private stochastic gradient descent (DP-SGD) has been widely adopted in deep learning to provide rigorously defined privacy, which requires gradient clipping to bound the maximum norm of individual gradients and additive…

Machine Learning · Computer Science 2023-06-29 Junyi Zhu , Matthew B. Blaschko

We show that high-accuracy guarantees for log-concave sampling -- that is, iteration and query complexities which scale as $\mathrm{poly}\log(1/\delta)$, where $\delta$ is the desired target accuracy -- are achievable using stochastic…

Statistics Theory · Mathematics 2026-05-18 Fan Chen , Sinho Chewi , Constantinos Daskalakis , Alexander Rakhlin

We prove quantitative convergence rates at which discrete Langevin-like processes converge to the invariant distribution of a related stochastic differential equation. We study the setup where the additive noise can be non-Gaussian and…

Machine Learning · Computer Science 2020-11-20 Xiang Cheng , Dong Yin , Peter L. Bartlett , Michael I. Jordan

Most results on Stochastic Gradient Descent (SGD) in the convex and smooth setting are presented under the form of bounds on the ergodic function value gap. It is an open question whether bounds can be derived directly on the last iterate…

Optimization and Control · Mathematics 2025-07-21 Guillaume Garrigos , Daniel Cortild , Lucas Ketels , Juan Peypouquet

We propose an extragradient method with stepsizes bounded away from zero for stochastic variational inequalities requiring only pseudo-monotonicity. We provide convergence and complexity analysis, allowing for an unbounded feasible set,…

Optimization and Control · Mathematics 2017-03-02 Alfredo Iusem , Alejandro Jofré , Roberto I. Oliveira , Philip Thompson

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

We present two easy-to-implement gradient-free/zeroth-order methods to optimize a stochastic non-smooth function accessible only via a black-box. The methods are built upon efficient first-order methods in the heavy-tailed case, i.e., when…

Optimization and Control · Mathematics 2023-08-25 Nikita Kornilov , Alexander Gasnikov , Pavel Dvurechensky , Darina Dvinskikh

In recent years, there has been considerable interest in designing stochastic first-order algorithms to tackle finite-sum smooth minimax problems. To obtain the gradient estimates, one typically relies on the uniform…

Optimization and Control · Mathematics 2024-10-08 Xia Jiang , Linglingzhi Zhu , Anthony Man-Cho So , Shisheng Cui , Jian Sun

We aim to make stochastic gradient descent (SGD) adaptive to (i) the noise $\sigma^2$ in the stochastic gradients and (ii) problem-dependent constants. When minimizing smooth, strongly-convex functions with condition number $\kappa$, we…

Optimization and Control · Mathematics 2026-03-24 Sharan Vaswani , Benjamin Dubois-Taine , Reza Babanezhad

In this paper, we study federated optimization for solving stochastic variational inequalities (VIs), a problem that has attracted growing attention in recent years. Despite substantial progress, a significant gap remains between existing…

Machine Learning · Computer Science 2026-02-11 Guanghui Wang , Satyen Kale

Analysis of Stochastic Gradient Descent (SGD) and its variants typically relies on the assumption of uniformly bounded variance, a condition that frequently fails in practical non-convex settings, such as neural network training, as well as…

Machine Learning · Computer Science 2026-04-21 Arda Fazla , Ege C. Kaya , Antesh Upadhyay , Abolfazl Hashemi

Various gradient compression schemes have been proposed to mitigate the communication cost in distributed training of large scale machine learning models. Sign-based methods, such as signSGD, have recently been gaining popularity because of…

Optimization and Control · Mathematics 2021-06-25 Mher Safaryan , Peter Richtárik

In this work, we conduct the first systematic study of stochastic variational inequality (SVI) and stochastic saddle point (SSP) problems under the constraint of differential privacy (DP). We propose two algorithms: Noisy Stochastic…

Optimization and Control · Mathematics 2022-04-04 Digvijay Boob , Cristóbal Guzmán

Distributed and federated learning algorithms and techniques associated primarily with minimization problems. However, with the increase of minimax optimization and variational inequality problems in machine learning, the necessity of…

Optimization and Control · Mathematics 2024-06-04 Siqi Zhang , Sayantan Choudhury , Sebastian U Stich , Nicolas Loizou

To lower the communication complexity of federated min-max learning, a natural approach is to utilize the idea of infrequent communications (through multiple local updates) same as in conventional federated learning. However, due to the…

Machine Learning · Computer Science 2022-12-27 Haibo Yang , Zhuqing Liu , Xin Zhang , Jia Liu

Two of the most prominent algorithms for solving unconstrained smooth games are the classical stochastic gradient descent-ascent (SGDA) and the recently introduced stochastic consensus optimization (SCO) [Mescheder et al., 2017]. SGDA is…

Machine Learning · Computer Science 2021-11-05 Nicolas Loizou , Hugo Berard , Gauthier Gidel , Ioannis Mitliagkas , Simon Lacoste-Julien

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