mlsanityData to 7 Oct 2026

From Nesterov's Estimate Sequence to Riemannian Acceleration

arXiv 2001.08876 ↗First posted 24 Jan 2020math.OC stat.MLcited by 24

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Abstract (arXiv)

We propose the first global accelerated gradient method for Riemannian manifolds. Toward establishing our result we revisit Nesterov's estimate sequence technique and develop an alternative analysis for it that may also be of independent interest. Then, we extend this analysis to the Riemannian setting, localizing the key difficulty due to non-Euclidean structure into a certain ``metric distortion.'' We control this distortion by developing a novel geometric inequality, which permits us to propose and analyze a Riemannian counterpart to Nesterov's accelerated gradient method.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 Jan 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 6; 2023: 7; 2024: 3; 2025: 3; 2026: 2.

24 papers.

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  1. 2023A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifoldcited by 21
  2. 2023Infeasible Deterministic, Stochastic, and Variance-Reduction Algorithms for Optimization under Orthogonality Constraintscited by 18
  3. 2022Momentum Stiefel Optimizer, with Applications to Suitably-Orthogonal Attention, and Optimal Transportcited by 10
  4. 2023Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learningcited by 10
  5. 2022Sion's Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithmcited by 9
  6. 2024Optimization without Retraction on the Random Generalized Stiefel Manifoldcited by 7
  7. 2023Minimizing Dynamic Regret on Geodesic Metric Spacescited by 6
  8. 2021Optimization on manifolds: A symplectic approachcited by 5
  9. 2022Riemannian accelerated gradient methods via extrapolationcited by 5
  10. 2021No-go Theorem for Acceleration in the Hyperbolic Planecited by 4
  11. 2022Accelerated Riemannian Optimization: Handling Constraints with a Prox to Bound Geometric Penaltiescited by 4
  12. 2023Riemannian Projection-free Online Learningcited by 4
12 more
  1. 2025Decentralized Online Riemannian Optimization Beyond Hadamard Manifoldscited by 4
  2. 2021Understanding Riemannian Acceleration via a Proximal Extragradient Frameworkcited by 3
  3. 2025Efficient Optimization with Orthogonality Constraint: a Randomized Riemannian Submanifold Methodcited by 3
  4. 2023Low-complexity subspace-descent over symmetric positive definite manifoldcited by 2
  5. 2026Natural gradient descent with momentumcited by 2
  6. 2022Riemannian Stochastic Gradient Method for Nested Composition Optimizationcited by 1
  7. 2022Rieoptax: Riemannian Optimization in JAXcited by 1
  8. 2023Extragradient Type Methods for Riemannian Variational Inequality Problemscited by 1
  9. 2024Quantitative Convergences of Lie Group Momentum Optimizerscited by 1
  10. 2024Learning-Rate-Free Stochastic Optimization over Riemannian Manifoldscited by 1
  11. 2025Quantum Optimization via Gradient-Based Hamiltonian Descentcited by 0
  12. 2026Riemannian Zeroth-Order Gradient Estimation with Structure-Preserving Metrics for Geodesically Incomplete Manifoldscited by 0