Revisiting the Role of Euler Numerical Integration on Acceleration and Stability in Convex Optimization
Abstract
Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often supposed to be linked to the quality of the integrator (accuracy, energy preservation, symplecticity). In this work, we propose a novel ordinary differential equation that questions this connection: both the explicit and the semi-implicit (a.k.a symplectic) Euler discretizations on this ODE lead to an accelerated algorithm for convex programming. Although semi-implicit methods are well-known in numerical analysis to enjoy many desirable features for the integration of physical systems, our findings show that these properties do not necessarily relate to acceleration.
Cite
Text
Zhang et al. "Revisiting the Role of Euler Numerical Integration on Acceleration and Stability in Convex Optimization." Artificial Intelligence and Statistics, 2021.Markdown
[Zhang et al. "Revisiting the Role of Euler Numerical Integration on Acceleration and Stability in Convex Optimization." Artificial Intelligence and Statistics, 2021.](https://mlanthology.org/aistats/2021/zhang2021aistats-revisiting/)BibTeX
@inproceedings{zhang2021aistats-revisiting,
title = {{Revisiting the Role of Euler Numerical Integration on Acceleration and Stability in Convex Optimization}},
author = {Zhang, Peiyuan and Orvieto, Antonio and Daneshmand, Hadi and Hofmann, Thomas and Smith, Roy S.},
booktitle = {Artificial Intelligence and Statistics},
year = {2021},
pages = {3979-3987},
volume = {130},
url = {https://mlanthology.org/aistats/2021/zhang2021aistats-revisiting/}
}