mlsanityData to 7 Oct 2026

Understanding Riemannian Acceleration via a Proximal Extragradient Framework

arXiv 2111.02763 ↗First posted 4 Nov 2021math.OC cs.LG stat.MLcited by 3

Not on the map. Why?

Abstract (arXiv)

We contribute to advancing the understanding of Riemannian accelerated gradient methods. In particular, we revisit Accelerated Hybrid Proximal Extragradient(A-HPE), a powerful framework for obtaining Euclidean accelerated methods citepmonteiro2013accelerated. Building on A-HPE, we then propose and analyze Riemannian A-HPE. The core of our analysis consists of two key components: (i) a set of new insights into Euclidean A-HPE itself; and (ii) a careful control of metric distortion caused by Riemannian geometry. We illustrate our framework by obtaining a few existing and new Riemannian accelerated gradient methods as special cases, while characterizing their acceleration as corollaries of our main results.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 19 of its 45 references that are in the map. First posted on arXiv 4 Nov 2021.

Builds on

19 of 45 references.

References · 19

  1. 2016First-order Methods for Geodesically Convex Optimizationcited by 92
  2. 2016Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifoldscited by 64
  3. 2014Linear Coupling: An Ultimate Unification of Gradient and Mirror Descentcited by 58
  4. 2019Escaping from saddle points on Riemannian manifoldscited by 33
  5. 2020Acceleration with a Ball Optimization Oraclecited by 31
  6. 2014Optimization Techniques on Riemannian Manifoldscited by 27
  7. 2020From Nesterov's Estimate Sequence to Riemannian Accelerationcited by 24
  8. 2017Oracle Complexity of Second-Order Methods for Smooth Convex Optimizationcited by 23
  9. 2018Adaptive regularization with cubics on manifoldscited by 17
  10. 2018Near-optimal method for highly smooth convex optimizationcited by 16
  11. 2020An accelerated first-order method for non-convex optimization on manifoldscited by 15
  12. 2018An Optimal High-Order Tensor Method for Convex Optimizationcited by 12
7 more
  1. 2017Accelerated Extra-Gradient Descent: A Novel Accelerated First-Order Methodcited by 8
  2. 2019Towards a theory of non-commutative optimization: geodesic first and second order methods for moment maps and polytopescited by 7
  3. 2019First order optimization methods based on Hessian-driven Nesterov accelerated gradient flowcited by 6
  4. 2021No-go Theorem for Acceleration in the Hyperbolic Planecited by 4
  5. 2021A Unifying Framework of Accelerated First-Order Approach to Strongly Monotone Variational Inequalitiescited by 3
  6. 2021Variants of the A-HPE and large-step A-HPE algorithms for strongly convex problems with applications to accelerated high-order tensor methodscited by 2
  7. 2021A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectivescited by 2

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Cited by year

Citing papers per year: 2022: 2; 2023: 1.

3 papers.

  1. 2022Riemannian accelerated gradient methods via extrapolationcited by 5
  2. 2023Last-Iterate Convergence of Adaptive Riemannian Gradient Descent for Equilibrium Computationcited by 2
  3. 2022Changes from Classical Statistics to Modern Statistics and Data Sciencecited by 0