Vanilla SGD with Momentum Survives Heavy-Tailed Noise: Convergence Analysis without Gradient Clipping or Normalization
Stochastic gradient descent (SGD) is a cornerstone of modern optimization. While its performance under heavy-tailed noise is often addressed through specialized modifications such as gradient clipping or normalization, we investigate a more fundamental question: how does vanilla SGD, particularly with momentum, perform in the presence of heavy-tailed noise? In this paper, we refine existing convergence results for vanilla SGD and, more importantly, provide the first comprehensive convergence analysis of vanilla SGD with momentum for strongly convex, convex, and nonconvex objectives, without employing any gradient control mechanisms. Our results demonstrate that the obtained convergence ra...
| Authors | Ryusei Yamada, Naoki Sato, Hideaki Iiduka |
|---|---|
| Primary category | cs.LG |
| Published | 9 July 2026 |
| Last updated at source | 13 August 2026 |
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