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

Hiroyuki Kasai, Hiroyuki Sato, Bamdev Mishra

研究成果: Paper査読

9 被引用数 (Scopus)

抄録

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.

本文言語English
ページ269-278
ページ数10
出版ステータスPublished - 2018
外部発表はい
イベント21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018 - Playa Blanca, Lanzarote, Canary Islands, Spain
継続期間: 2018 4月 92018 4月 11

Conference

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

ASJC Scopus subject areas

  • 統計学および確率
  • 人工知能

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