SIGNALAI·Jun 2, 2026, 4:00 AMSignal75Medium term

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

Source: arXiv cs.LG

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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. To manage this realistic and challenging setting, new mechanisms, such as gradient clipping and gradient normalization, have been introduced to ensure the convergence of first-order algorithms. However, adaptive gradient methods, a famous class of modern optimizers that includes popular $\mathtt{Adam}$ and $\mathtt{AdamW}$, often perform well even without any extra operations mentioned above. It is therefore natural

Why this matters
Why now

The paper addresses a current challenge in deep learning optimization, particularly the robustness of adaptive gradient methods like AdaGrad in environments with heavy-tailed noise, which is increasingly prevalent in modern machine learning tasks.

Why it’s important

Improved understanding and theoretical guarantees for optimization algorithms under realistic noise conditions enhance the reliability and efficiency of AI training, directly impacting performance and resource utilization.

What changes

This research provides theoretical backing for the observed empirical success of adaptive gradient methods in challenging noise environments, potentially guiding algorithm design and selection for robust AI systems.

Winners
  • · AI researchers and developers
  • · Companies deploying AI models
  • · Edge AI applications
  • · Hardware providers with efficient model training
Losers
  • · Developers solely relying on naive SGD in noisy environments
Second-order effects
Direct

More stable and efficient training of deep learning models in real-world scenarios with less need for manual hyperparameter tuning.

Second

Accelerated development and deployment of robust AI applications, especially in areas with inherently noisy data or computational environments.

Third

Reduced compute costs and energy consumption for training sophisticated AI models, as optimization becomes more efficient and less prone to divergence.

Editorial confidence: 90 / 100 · Structural impact: 40 / 100
Original report

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Read at arXiv cs.LG
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