A Riemannian Accelerated Proximal Extragradient Framework and its Implications

W e 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 metho ds [ 29 ]. 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 g eometry . W e illustrate our framework by obtaining a few existing and new Riemannian acc elerated gradient methods as special cases, while characterizing their accelerat ion as corollaries of our main results.