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

2 Citations (Scopus)

Abstract

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)
Pages3912-3935
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
Volume6

Conference

Conference35th International Conference on Machine Learning, ICML 2018
CountrySweden
CityStockholm
Period18/7/1018/7/15

ASJC Scopus subject areas

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

Cite this

Kasai, H., Sato, H., & Mishra, B. (2018). Riemannian Stochastic recursive gradient algorithm with retraction and vector transport and its convergence analysis. In J. Dy, & A. Krause (Eds.), 35th International Conference on Machine Learning, ICML 2018 (pp. 3912-3935). (35th International Conference on Machine Learning, ICML 2018; Vol. 6). International Machine Learning Society (IMLS).