Riemannian stochastic quasi-Newton algorithm with variance reduction and its convergence analysis

Hiroyuki Kasai, Hiroyuki Sato, Bamdev Mishra

Research output: Contribution to conferencePaper

5 Citations (Scopus)

Abstract

Stochastic variance reduction algorithms have recently become popular for minimizing the average value of a large but finite number of loss functions. This paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR). We present convergence analyses of the R-SQN-VR on both non-convex and retraction strongly convex functions with retraction and vector transport. The proposed algorithm is tested on the Riemannian centroid computation on the symmetric positive-definite manifold and the low-rank matrix completion on the Grassmann manifold. In all cases, the proposed algorithm outperforms the state-of-the-art Riemannian batch and stochastic gradient algorithms.

Original languageEnglish
Pages269-278
Number of pages10
Publication statusPublished - 2018
Externally publishedYes
Event21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018 - Playa Blanca, Lanzarote, Canary Islands, Spain
Duration: 2018 Apr 92018 Apr 11

Conference

Conference21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018
CountrySpain
CityPlaya Blanca, Lanzarote, Canary Islands
Period18/4/918/4/11

ASJC Scopus subject areas

  • Statistics and Probability
  • Artificial Intelligence

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    Kasai, H., Sato, H., & Mishra, B. (2018). Riemannian stochastic quasi-Newton algorithm with variance reduction and its convergence analysis. 269-278. Paper presented at 21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018, Playa Blanca, Lanzarote, Canary Islands, Spain.