Adam Optimizer Convergence Analyzed Under Heavy-Tailed Noise
Key takeaways
- Adam optimizer's convergence is guaranteed even with heavy-tailed noise.
- Its convergence rate is suboptimal, even in standard bounded-variance cases.
- Knowing the domain radius can improve Adam's convergence speed.
- The findings offer new theoretical insights into Adam's behavior in challenging environments.
Who benefits
Summary
This research provides the first convergence guarantees for the Adam optimizer when dealing with heavy-tailed stochastic noise, a common scenario in deep learning. It reveals that Adam converges to stationary points but with suboptimal iteration complexity, even in bounded-variance cases.
Why it matters
Professionals using Adam for deep learning models, especially in noisy or complex data environments, gain a deeper understanding of its theoretical performance limits and potential inefficiencies. This insight can guide hyperparameter tuning and algorithm selection for more robust model training.
How to implement this in your domain
- 1Review current Adam implementations for potential heavy-tailed noise issues in data.
- 2Consider alternative optimizers or Adam variants if convergence speed is critical in noisy settings.
- 3Experiment with explicit domain radius control if applicable to improve Adam's convergence rate.
- 4Monitor training stability and convergence behavior more closely in applications prone to heavy-tailed noise.
Original post by Yijiang Pang
"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. While several Adam variants are known to achieve optimal iteration complexity in bounded-variance non…"
View on XOriginally posted by Yijiang Pang on X · view source
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