Riemannian Stochastic recursive gradient algorithm with retraction and vector transport and its convergence analysis

Hiroyuki Kasai, Hiroyuki Sato, Bamdev Mishra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)


Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions on a Riemannian manifold. The present paper proposes a Riemannian stochastic recursive gradient algorithm (R-SRG), which does not require the inverse of retraction between two distant iterates on the manifold. Convergence analyses of R-SRG are performed on both retractionconvex and non-convex functions under computationally efficient retraction and vector transport operations. The key challenge is analysis of the influence of vector transport along the retraction curve. Numerical evaluations reveal that R-SRG competes well with state-of-the-art Riemannian batch and stochastic gradient algorithms.

Original languageEnglish
Title of host publication35th International Conference on Machine Learning, ICML 2018
EditorsJennifer Dy, Andreas Krause
PublisherInternational Machine Learning Society (IMLS)
Number of pages24
ISBN (Electronic)9781510867963
Publication statusPublished - 2018
Externally publishedYes
Event35th International Conference on Machine Learning, ICML 2018 - Stockholm, Sweden
Duration: 2018 Jul 102018 Jul 15

Publication series

Name35th International Conference on Machine Learning, ICML 2018


Conference35th International Conference on Machine Learning, ICML 2018

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Human-Computer Interaction
  • Software

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