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# From Nesterov’s Estimate Sequence to Riemannian Acceleration

*Proceedings of Thirty Third Conference on Learning Theory*, PMLR 125:84-118, 2020.

#### Abstract

We propose the first global accelerated gradient method for Riemannian manifolds. Toward establishing our results, we revisit Nesterov’s estimate sequence technique and develop a conceptually simple alternative from first principles. We then extend our analysis to Riemannian acceleration, localizing the key difficulty into “metric distortion.” We control this distortion via a novel geometric inequality, which enables us to formulate and analyze global Riemannian acceleration.