On Acceleration with Noise-Corrupted Gradients
Michael Cohen, Jelena Diakonikolas, Lorenzo Orecchia
Abstract
Accelerated algorithms have broad applications in large-scale optimization, due to their generality and fast convergence. However, their stability in the practical setting of noise-corrupted gradient oracles is not well-understood. This paper provides two main technical contributions: (i) a new accelerated method AGDP that generalizes Nesterov’s AGD and improves on the recent method AXGD (Diakonikolas & Orecchia, 2018), and (ii) a theoretical study of accelerated algorithms under noisy and inexact gradient oracles, which is supported by numerical experiments. This study leverages the simplicity of AGDP and its analysis to clarify the interaction between noise and acceleration and to suggest modifications to the algorithm that reduce the mean and variance of the error incurred due to the gradient noise.
BibTeX
@InProceedings{pmlr-v80-cohen18a,
title = {On Acceleration with Noise-Corrupted Gradients},
author = {Cohen, Michael and Diakonikolas, Jelena and Orecchia, Lorenzo},
booktitle = {Proceedings of the 35th International Conference on Machine Learning},
pages = {1019--1028},
year = {2018},
editor = {Dy, Jennifer and Krause, Andreas},
volume = {80},
series = {Proceedings of Machine Learning Research},
month = {10--15 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v80/cohen18a/cohen18a.pdf},
url = {https://proceedings.mlr.press/v80/cohen18a.html},
abstract = {Accelerated algorithms have broad applications in large-scale optimization, due to their generality and fast convergence. However, their stability in the practical setting of noise-corrupted gradient oracles is not well-understood. This paper provides two main technical contributions: (i) a new accelerated method AGDP that generalizes Nesterov’s AGD and improves on the recent method AXGD (Diakonikolas & Orecchia, 2018), and (ii) a theoretical study of accelerated algorithms under noisy and inexact gradient oracles, which is supported by numerical experiments. This study leverages the simplicity of AGDP and its analysis to clarify the interaction between noise and acceleration and to suggest modifications to the algorithm that reduce the mean and variance of the error incurred due to the gradient noise.}
}