Understanding Riemannian Acceleration via a Proximal Extragradient Framework
In the Thirty-Fifth Annual Conference on Learning Theory · 2022
Abstract
We contribute to advancing the understanding of Riemannian accelerated gradient methods. In particular, we revisit Accelerated Hybrid Proximal Extragradient(A-HPE), a powerful framework for obtaining Euclidean accelerated methods \citep{monteiro2013accelerated}. Building on A-HPE, we then propose and analyze Riemannian A-HPE. The core of our analysis consists of two key components (i) a set of new insights into Euclidean A-HPE itself; and (ii) a careful control of metric distortion caused by Riemannian geometry. We illustrate our framework by obtaining a few existing and new Riemannian accelerated gradient methods as special cases, while characterizing their acceleration as corollaries of our main results.
Cite
@article{jin2021riemannian,
title={Understanding Riemannian Acceleration via a Proximal Extragradient Framework},
author={Jin, Jikai and Sra, Suvrit},
journal={arXiv preprint arXiv:2111.02763},
year={2021}
}