arXiv Machine Learning

In-Expectation Convergence of Stochastic Gradient Methods under Heavy-Tailed Noise

arXiv:2606. 00520v1 Announce Type: cross Abstract: Many stochastic gradient methods are believed not to converge when the noise in stochastic gradients has only a finite $p$-th moment for $p\in\left(1,2\right)$, a setting known as the heavy-tailed noise assumption.

arXiv Machine Learning

Sep 14

Almost Sure Convergence Analysis of Stochastic Gradient Methods with Clipping and Additive Noise

The paper proves that stochastic gradient descent with gradient clipping and additive Gaussian noise (SGD‑CN) converges almost surely under smoothness and bounded noise assumptions, given standard decaying step sizes. The analysis extends to momentum variants such as the stochastic heavy ball and Nesterov's accelerated gradient, showing that careful energy constructions yield similar guarantees. These results provide stronger theoretical foundations for understanding the pathwise behaviour of clipped stochastic gradient methods in both convex and nonconvex regimes.

By Amartya Mukherjee, Jun Liu

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arXiv Machine Learning

Jul 10

Vanilla SGD with Momentum Survives Heavy-Tailed Noise: Convergence Analysis without Gradient Clipping or Normalization

arXiv:2607. 08104v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is a cornerstone of modern optimization.

By Ryusei Yamada, Naoki Sato, Hideaki Iiduka

arXiv AI

Sep 10

The Role of Gradient Modification in Heavy-Tailed Nonconvex Stochastic Min-Max Optimization

arXiv:2609.06064v1 Announce Type: cross Abstract: Stochastic min-max optimization has attracted increasing attention due to its applications in modern machine learning, while existing theoretical stu...

By Tianxi Zhu, Yi Xu, Xiangyang Ji

arXiv Machine Learning

Jun 2

Can Adaptive Gradient Methods Converge under Heavy-Tailed Noise? A Case Study of AdaGrad

arXiv:2605. 18694v2 Announce Type: replace-cross Abstract: Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process.

By Zijian Liu

arXiv Statistics ML

Aug 26

Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise

arXiv:2506.04192v4 Announce Type: replace-cross Abstract: Stochastic Frank-Wolfe is a classical optimization method for solving constrained optimization problems. On the other hand, recent optimizers...

By Maria-Eleni Sfyraki, Jun-Kun Wang

arXiv Machine Learning

Sep 14

Convergence of Stochastic Gradient Methods under Heavy-Tailed Noise and H\"{o}lder Smoothness

arXiv:2609. 12785v1 Announce Type: new Abstract: Classical convergence guarantees for stochastic gradient methods typically assume Lipschitz-smooth objectives and finite-variance gradient noise, both frequently violated in practice.

By Misbah Uz Zaman, Anirbit Mukherjee

arXiv Machine Learning

Sep 22

Accelerated stochastic first-order method for convex optimization under heavy-tailed noise

arXiv:2510.11676v2 Announce Type: replace-cross Abstract: We study convex composite optimization problems, where the objective function is given by the sum of a prox-friendly function and a convex fu...

By Chuan He, Bowen Li, Zhaosong Lu

arXiv Machine Learning

Jun 3

Bregman meets L\'evy: Stochastic mirror descent with heavy-tailed noise in continuous and discrete time

arXiv:2606. 03769v1 Announce Type: cross Abstract: We study the robustness of stochastic mirror descent (SMD) under heavy-tailed noise, focusing on whether the method retains its convergence guarantees when run with infinite-variance stochastic gradient input.

By Pierre-Louis Cauvin, Panayotis Mertikopoulos

arXiv Machine Learning

Jul 31

The Convergence Behavior of Adam under Heavy-Tailed Noise

arXiv:2607. 27383v1 Announce Type: new Abstract: We establish the first convergence guarantees for the plain vector-form \emph{Adam} optimizer under heavy-tailed stochastic noise.

By Yijiang Pang

arXiv Machine Learning

4d ago

High-Probability Convergence of Clipped SGD under Heavy-Tailed Noise and $(L_0,L_1)$-Smoothness

arXiv:2505.20817v3 Announce Type: replace-cross Abstract: Gradient clipping is widely used in language-model training to control heavy-tailed gradient noise and can improve convergence guarantees ove...

By Taha El Bakkali El Kadi, Savelii Chezhegov, Aleksandr Beznosikov, Samuel Horv\'ath, Eduard Gorbunov

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arXiv Machine Learning

Jun 24

Accelerated Stochastic Min-Max Optimization Based on Bias-corrected Momentum

arXiv:2406. 13041v3 Announce Type: replace Abstract: Lower-bound analyses for nonconvex strongly-concave minimax optimization problems have shown that stochastic first-order algorithms require at least $\mathcal{O}(\varepsilon^{-4})$ sample complexity to find an $\varepsilon$-stationary point.

By Haoyuan Cai, Sulaiman A. Alghunaim, Ali H. Sayed

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arXiv Machine Learning

Jul 2

Towards Weaker Variance Assumptions for Stochastic Optimization

arXiv:2504. 09951v2 Announce Type: replace-cross Abstract: We revisit a classical assumption for analyzing stochastic gradient algorithms where the squared norm of the stochastic subgradient (or the variance for smooth problems) is allowed to grow as fast as the squared norm of the optimization variable.

By Ahmet Alacaoglu, Yura Malitsky, Stephen J. Wright

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