Understanding Riemannian Acceleration via a Proximal Extragradient Framework

Jikai Jin; Suvrit Sra

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arXiv · 2111.02763

Understanding Riemannian Acceleration via a Proximal Extragradient Framework

Jikai Jin·Suvrit Sra

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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.

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Jikai Jin, Suvrit Sra. 2021-11-04. Understanding Riemannian Acceleration via a Proximal Extragradient Framework. https://arxiv.org/abs/2111.02763

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