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Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep…

Machine Learning · Statistics 2019-06-24 Thanh Huy Nguyen , Umut Şimşekli , Mert Gürbüzbalaban , Gaël Richard

We introduce a general framework for nonlinear stochastic gradient descent (SGD) for the scenarios when gradient noise exhibits heavy tails. The proposed framework subsumes several popular nonlinearity choices, like clipped, normalized,…

Optimization and Control · Mathematics 2022-04-07 Dusan Jakovetic , Dragana Bajovic , Anit Kumar Sahu , Soummya Kar , Nemanja Milosevic , Dusan Stamenkovic

This paper considers the problem of asynchronous stochastic nonconvex optimization with heavy-tailed gradient noise and arbitrarily heterogeneous computation times across workers. We propose an asynchronous normalized stochastic gradient…

Optimization and Control · Mathematics 2026-01-28 Yidong Wu , Luo Luo

We introduce a clipping strategy for Stochastic Gradient Descent (SGD) which uses quantiles of the gradient norm as clipping thresholds. We prove that this new strategy provides a robust and efficient optimization algorithm for smooth…

Machine Learning · Statistics 2024-10-15 Ibrahim Merad , Stéphane Gaïffas

This paper is devoted to the problem of determining the concentration bounds that are achievable in non-parametric regression. We consider the setting where features are supported on a bounded subset of $\mathbb{R}^d$, the regression…

Statistics Theory · Mathematics 2024-12-02 Anna Ben-Hamou , Arnaud Guyader

Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…

Methodology · Statistics 2025-09-16 Xiaoyu Zhang , Di Wang , Guodong Li , Defeng Sun

Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Bruce Allen , Jolien D. E. Creighton , Eanna E. Flanagan , Joseph D. Romano

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

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

We study large deviation upper bounds and mean-squared error (MSE) guarantees of a general framework of nonlinear stochastic gradient methods in the online setting, in the presence of heavy-tailed noise. Unlike existing works that rely on…

Machine Learning · Computer Science 2025-03-25 Aleksandar Armacki , Shuhua Yu , Dragana Bajovic , Dusan Jakovetic , Soummya Kar

Stochastic optimization is fundamental to modern machine learning. Recent research has extended the study of stochastic first-order methods (SFOMs) from light-tailed to heavy-tailed noise, which frequently arises in practice, with clipping…

Machine Learning · Computer Science 2025-12-17 Chuan He

Training instabilities such as loss spikes are frequently the result of stochastic gradient noise. Because of rare expressions in language training data, and multiple layer composition, the noise impact is heavy-tailed and survives…

Machine Learning · Computer Science 2026-05-28 Zitao Song , Cedar Site Bai , Zhe Zhang , Brian Bullins , David F. Gleich

Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…

Applications · Statistics 2023-01-20 Pooja Algikar , Lamine Mili

Gradient compression has surfaced as a key technique to address the challenge of communication efficiency in distributed learning. In distributed deep learning, however, it is observed that gradient distributions are heavy-tailed, with…

Machine Learning · Computer Science 2024-02-07 Guangfeng Yan , Tan Li , Yuanzhang Xiao , Hanxu Hou , Linqi Song

A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized. Scale-invariant methods become important because their normalized layerwise updates can not only support hyperparameter…

Optimization and Control · Mathematics 2026-05-19 Jiayu Zhang , Tianyi Lin

We study convex composite optimization problems, where the objective function is given by the sum of a prox-friendly function and a convex function whose subgradients are estimated under heavy-tailed noise. Existing work often employs…

Optimization and Control · Mathematics 2025-10-14 Chuan He , Zhaosong Lu

In recent years, non-convex optimization problems are more often described by generalized $(L_0, L_1)$-smoothness assumption rather than standard one. Meanwhile, severely corrupted data used in these problems has increased the demand for…

Optimization and Control · Mathematics 2025-05-28 Nikita Kornilov , Philip Zmushko , Andrei Semenov , Mark Ikonnikov , Alexander Gasnikov , Alexander Beznosikov

We propose a new method to approximate the posterior distribution of probabilistic programs by means of computing guaranteed bounds. The starting point of our work is an interval-based trace semantics for a recursive, higher-order…

Programming Languages · Computer Science 2022-06-07 Raven Beutner , Luke Ong , Fabian Zaiser

In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…

Machine Learning · Computer Science 2019-03-22 Anastasios Tsiamis , George J. Pappas

This paper considers the smooth bilevel optimization in which the lower-level problem is strongly convex and the upper-level problem is possibly nonconvex. We focus on the stochastic setting where the algorithm can access the unbiased…

Machine Learning · Computer Science 2025-12-16 Zhuanghua Liu , Luo Luo