A Variational Perspective on High-Resolution ODEs
Abstract
We consider unconstrained minimization of smooth convex functions. We propose a novel variational perspective using forced Euler-Lagrange equation that allows for studying high-resolution ODEs. Through this, we obtain a faster convergence rate for gradient norm minimization using Nesterov's accelerated gradient method. Additionally, we show that Nesterov's method can be interpreted as a rate-matching discretization of an appropriately chosen high-resolution ODE. Finally, using the results from the new variational perspective, we propose a stochastic method for noisy gradients. Several numerical experiments compare and illustrate our stochastic algorithm with state of the art methods.
Cite
@article{arxiv.2311.02002,
title = {A Variational Perspective on High-Resolution ODEs},
author = {Hoomaan Maskan and Konstantinos C. Zygalakis and Alp Yurtsever},
journal= {arXiv preprint arXiv:2311.02002},
year = {2023}
}
Comments
37th Annual Conference on Neural Information Processing Systems (NeurIPS 2023)