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Towards Riemannian Accelerated Gradient Methods
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We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm (RAGD), and show that for geodesically smooth and strongly convex problems, within a neighborhood of the minimizer whose radius depends on the condition number as well as the sectional curvature of the manifold, RAGD converges to the minimizer with acceleration. Unlike the algorithm in (Liu et al., 2017) that requires the exact solution to a nonlinear equation which in turn may be intractable, our algorithm is constructive and computationally tractable. Our proof exploits a new estimate sequence and a novel bound on the nonlinear metric distortion, both ideas may be of independent interest.
Forward citations
Cited by 2 Pith papers
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The authors derive and analyze accelerated Nesterov-type gradient flows in probability space under four information metrics and use them to build faster mean-field MCMC sampling algorithms.
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