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Special Properties of Gradient Descent with Large Learning Rates

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Version 2 2023-12-14, 12:33
Version 1 2023-11-29, 18:24
conference contribution
posted on 2023-12-14, 12:33 authored by Amirkeivan Mohtashami, Martin Jaggi, Sebastian StichSebastian Stich
When training neural networks, it has been widely observed that a large step size is essential in stochastic gradient descent (SGD) for obtaining superior models. However, the effect of large step sizes on the success of SGD is not well understood theoretically. Several previous works have attributed this success to the stochastic noise present in SGD. However, we show through a novel set of experiments that the stochastic noise is not sufficient to explain good non-convex training, and that instead the effect of a large learning rate itself is essential for obtaining best performance.We demonstrate the same effects also in the noise-less case, i.e. for full-batch GD. We formally prove that GD with large step size ---on certain non-convex function classes --- follows a different trajectory than GD with a small step size, which can lead to convergence to a global minimum instead of a local one. Our settings provide a framework for future analysis which allows comparing algorithms based on behaviors that can not be observed in the traditional settings.

History

Preferred Citation

Amirkeivan Mohtashami, Martin Jaggi and Sebastian Stich. Special Properties of Gradient Descent with Large Learning Rates. In: International Conference on Machine Learning (ICML). 2023.

Primary Research Area

  • Trustworthy Information Processing

Name of Conference

International Conference on Machine Learning (ICML)

Legacy Posted Date

2023-06-30

Open Access Type

  • Green

BibTeX

@inproceedings{cispa_all_3977, title = "Special Properties of Gradient Descent with Large Learning Rates", author = "Mohtashami, Amirkeivan and Jaggi, Martin and Stich, Sebastian U.", booktitle="{International Conference on Machine Learning (ICML)}", year="2023", }

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