A Riemannian Accelerated Proximal Extragradient Framework and its Implications
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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 Accelerated Hybrid Proximal Extragradient (A-HPE) method of <cit.>, 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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