  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.

Optimization and Control;Machine Learning;Machine Learning