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Towards Riemannian Accelerated Gradient Methods

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arxiv 1806.02812 v1 pith:UZ74PZR3 submitted 2018-06-07 math.OC cs.LG

classification math.OCcs.LG
keywords algorithmacceleratedgradientminimizernonlinearragdriemannianacceleration
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 33 citations worldwide. Full citation record

  1. Accelerated Information Gradient flow

    math.OC 2019-09 conditional novelty 6.0 of 10

    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.

  2. Local Linear Convergence of Infeasible Optimization with Orthogonal Constraints

    math.OC 2024-12 conditional novelty 5.0 of 10

    The landing algorithm converges linearly near local minima for smooth non-convex optimization on the Stiefel manifold under a local Riemannian PŁ condition.

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