A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
Abstract
We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov's accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov's scheme and thus can serve as a tool for analysis. We show that the continuous time ODE allows for a better understanding of Nesterov's scheme. As a byproduct, we obtain a family of schemes with similar convergence rates. The ODE interpretation also suggests restarting Nesterov's scheme leading to an algorithm, which can be rigorously proven to converge at a linear rate whenever the objective is strongly convex.
Cite
Text
Su et al. "A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights." Journal of Machine Learning Research, 2016.Markdown
[Su et al. "A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights." Journal of Machine Learning Research, 2016.](https://mlanthology.org/jmlr/2016/su2016jmlr-differential/)BibTeX
@article{su2016jmlr-differential,
title = {{A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights}},
author = {Su, Weijie and Boyd, Stephen and Candès, Emmanuel J.},
journal = {Journal of Machine Learning Research},
year = {2016},
pages = {1-43},
volume = {17},
url = {https://mlanthology.org/jmlr/2016/su2016jmlr-differential/}
}