Breaking the Heavy-Tailed Noise Barrier in Stochastic Optimization Problems
Abstract
We consider stochastic optimization problems with heavy-tailed noise with structured density. For such problems, we show that it is possible to get faster rates of convergence than $O(K^{-2(\alpha - 1) / \alpha})$, when the stochastic gradients have finite $\alpha$-th moment, $\alpha \in (1, 2]$. In particular, our analysis allows the noise norm to have an unbounded expectation. To achieve these results, we stabilize stochastic gradients, using smoothed medians of means. We prove that the resulting estimates have negligible bias and controllable variance. This allows us to carefully incorporate them into clipped-SGD and clipped-SSTM and derive new high-probability complexity bounds in the considered setup.
Cite
Text
Puchkin et al. "Breaking the Heavy-Tailed Noise Barrier in Stochastic Optimization Problems." Artificial Intelligence and Statistics, 2024.Markdown
[Puchkin et al. "Breaking the Heavy-Tailed Noise Barrier in Stochastic Optimization Problems." Artificial Intelligence and Statistics, 2024.](https://mlanthology.org/aistats/2024/puchkin2024aistats-breaking/)BibTeX
@inproceedings{puchkin2024aistats-breaking,
title = {{Breaking the Heavy-Tailed Noise Barrier in Stochastic Optimization Problems}},
author = {Puchkin, Nikita and Gorbunov, Eduard and Kutuzov, Nickolay and Gasnikov, Alexander},
booktitle = {Artificial Intelligence and Statistics},
year = {2024},
pages = {856-864},
volume = {238},
url = {https://mlanthology.org/aistats/2024/puchkin2024aistats-breaking/}
}