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
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: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: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: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: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