ICML 2020poster57 citations
Stochastic Gradient and Langevin Processes
Xiang Cheng, Dong Yin, Peter Bartlett, Michael Jordan
Abstract
We prove quantitative convergence rates at which discrete Langevin-like processes converge to the invariant distribution of a related stochastic differential equation. We study the setup where the additive noise can be non-Gaussian and state-dependent and the potential function can be non-convex. We show that the key properties of these processes depend on the potential function and the second moment of the additive noise. We apply our theoretical findings to studying the convergence of Stochastic Gradient Descent (SGD) for non-convex problems and corroborate them with experiments using SGD to train deep neural networks on the CIFAR-10 dataset.
BibTeX
@InProceedings{pmlr-v119-cheng20e,
title = {Stochastic Gradient and {L}angevin Processes},
author = {Cheng, Xiang and Yin, Dong and Bartlett, Peter and Jordan, Michael},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {1810--1819},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/cheng20e/cheng20e.pdf},
url = {https://proceedings.mlr.press/v119/cheng20e.html},
abstract = {We prove quantitative convergence rates at which discrete Langevin-like processes converge to the invariant distribution of a related stochastic differential equation. We study the setup where the additive noise can be non-Gaussian and state-dependent and the potential function can be non-convex. We show that the key properties of these processes depend on the potential function and the second moment of the additive noise. We apply our theoretical findings to studying the convergence of Stochastic Gradient Descent (SGD) for non-convex problems and corroborate them with experiments using SGD to train deep neural networks on the CIFAR-10 dataset.}
}