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

2026-07-09 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new convergence analysis investigates how vanilla Stochastic Gradient Descent (SGD) with momentum performs under heavy-tailed noise, a common challenge in modern optimization. This research provides the first comprehensive convergence analysis for vanilla SGD with momentum across strongly convex, convex, and nonconvex objectives, critically, without relying on gradient clipping or normalization. The findings reveal that while vanilla methods do converge, their obtained rates are inferior to the optimal rates achieved by SGD variants that incorporate gradient control mechanisms. This demonstrates inherent limitations of vanilla SGD with momentum in such noisy environments, suggesting a trade-off between simplicity and performance. Theoretical results are substantiated by experiments conducted on synthetic functions.

Key takeaway

For AI scientists and machine learning engineers optimizing models in environments prone to heavy-tailed noise, you should recognize that vanilla SGD with momentum, while robust enough to converge, will likely yield suboptimal training speeds. If your application demands faster convergence or higher efficiency, prioritize implementing gradient clipping or normalization techniques. This understanding helps in selecting appropriate optimization strategies for robust and efficient model training.

Key insights

Vanilla SGD with momentum converges under heavy-tailed noise, but slower than clipped or normalized variants.

Principles

• Vanilla SGD with momentum can converge under heavy-tailed noise.
• Gradient control mechanisms improve convergence rates with heavy-tailed noise.

Topics

• Stochastic Gradient Descent
• SGD with Momentum
• Heavy-Tailed Noise
• Convergence Analysis
• Gradient Clipping
• Optimization Algorithms
• Nonconvex Optimization

Best for: Research Scientist, AI Scientist, AI Student

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.