A Riemannian Accelerated Proximal Extragradient Framework and its Implications
arxiv(2021)
摘要
The study of accelerated gradient methods in Riemannian optimization has recently witnessed notable progress. However, in contrast with the Euclidean setting, a systematic understanding of acceleration is still lacking in the Riemannian setting. We revisit the \emph{Accelerated Hybrid Proximal Extragradient} (A-HPE) method of \citet{monteiro2013accelerated}, a powerful framework for obtaining accelerated Euclidean methods. Subsequently, we propose a Riemannian version of A-HPE. The basis of our analysis of Riemannian A-HPE is a set of insights into Euclidean A-HPE, which we combine with a careful control of distortion caused by Riemannian geometry. We describe a number of Riemannian accelerated gradient methods as concrete instances of our framework.
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