mlsanityData to 14 Oct 2026

Riemannian accelerated gradient methods via extrapolation

arXiv 2208.06619 ↗First posted 13 Aug 2022math.OC cs.LG stat.MLcited by 5

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Abstract (arXiv)

In this paper, we propose a simple acceleration scheme for Riemannian gradient methods by extrapolating iterates on manifolds. We show when the iterates are generated from Riemannian gradient descent method, the accelerated scheme achieves the optimal convergence rate asymptotically and is computationally more favorable than the recently proposed Riemannian Nesterov accelerated gradient methods. Our experiments verify the practical benefit of the novel acceleration strategy.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 34 of its 77 references that are in the map. First posted on arXiv 13 Aug 2022.

Builds on

34 of 77 references.

References · 34

  1. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 684
  2. 2015A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insightscited by 206
  3. 2018Riemannian Adaptive Optimization Methodscited by 194
  4. 2013Manopt, a Matlab toolbox for optimization on manifoldscited by 113
  5. 2016A Variational Perspective on Accelerated Methods in Optimizationcited by 110
  6. 2016First-order Methods for Geodesically Convex Optimizationcited by 93
  7. 2016Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifoldscited by 64
  8. 2016Global rates of convergence for nonconvex optimization on manifoldscited by 62
  9. 2021Acceleration Methodscited by 48
  10. 2018Averaging Stochastic Gradient Descent on Riemannian Manifoldscited by 39
  11. 2019Escaping from saddle points on Riemannian manifoldscited by 33
  12. 2019A Continuous-time Perspective for Modeling Acceleration in Riemannian Optimizationcited by 25
22 more
  1. 2015Riemannian Dictionary Learning and Sparse Coding for Positive Definite Matricescited by 24
  2. 2020From Nesterov's Estimate Sequence to Riemannian Accelerationcited by 24
  3. 2016Regularized Nonlinear Accelerationcited by 18
  4. 2018Adaptive regularization with cubics on manifoldscited by 17
  5. 2020An accelerated first-order method for non-convex optimization on manifoldscited by 15
  6. 2020Geometry-aware Domain Adaptation for Unsupervised Alignment of Word Embeddingscited by 14
  7. 2013Dictionary Learning and Sparse Coding on Grassmann Manifolds: An Extrinsic Solutioncited by 13
  8. 2021Negative curvature obstructs acceleration for strongly geodesically convex optimization, even with exact first-order oraclescited by 12
  9. 2020Global Riemannian Acceleration in Hyperbolic and Spherical Spacescited by 10
  10. 2022Accelerated Gradient Methods for Geodesically Convex Optimization: Tractable Algorithms and Convergence Analysiscited by 10
  11. 2017A dual framework for low-rank tensor completioncited by 9
  12. 2021Manifold optimization for non-linear optimal transport problemscited by 8
  13. 2016Rapid Mixing of Geodesic Walks on Manifolds with Positive Curvaturecited by 7
  14. 2020Riemannian stochastic recursive momentum method for non-convex optimizationcited by 7
  15. 2022Riemannian block SPD coupling manifold and its application to optimal transportcited by 7
  16. 2019Accelerated Optimization With Orthogonality Constraintscited by 6
  17. 2021A Variational Formulation of Accelerated Optimization on Riemannian Manifoldscited by 5
  18. 2018Nonlinear Acceleration of Momentum and Primal-Dual Algorithmscited by 4
  19. 2021No-go Theorem for Acceleration in the Hyperbolic Planecited by 4
  20. 2019Low-rank approximations of hyperbolic embeddingscited by 3
  21. 2021Understanding Riemannian Acceleration via a Proximal Extragradient Frameworkcited by 3
  22. 2020A Simple Approach to Learning Unsupervised Multilingual Embeddingscited by 1

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Cited by year

Citing papers per year: 2022: 1; 2023: 0; 2024: 2; 2025: 2.

5 papers.

  1. 2024A Framework for Bilevel Optimization on Riemannian Manifoldscited by 3
  2. 2025Efficient Optimization with Orthogonality Constraint: a Randomized Riemannian Submanifold Methodcited by 3
  3. 2022Rieoptax: Riemannian Optimization in JAXcited by 1
  4. 2024Function Extrapolation with Neural Networks and Its Application for Manifoldscited by 1
  5. 2025Quantum Optimization via Gradient-Based Hamiltonian Descentcited by 0