Riemannian adaptive stochastic gradient algorithms on matrix manifolds

Hiroyuki Kasai*, Pratik Jawanpuria, Bamdev Mishra

*この研究の対応する著者

研究成果: Conference contribution

2 被引用数 (Scopus)

抄録

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the intrinsic nonlinear structure of the underlying manifold and the absence of a canonical coordinate system. In machine learning applications, however, most manifolds of interest are represented as matrices with notions of row and column subspaces. In addition, the implicit manifold-related constraints may also lie on such subspaces. For example, the Grassmann manifold is the set of column subspaces. To this end, such a rich structure should not be lost by transforming matrices to just a stack of vectors while developing optimization algorithms on manifolds. We propose novel stochastic gradient algorithms for problems on Riemannian matrix manifolds by adapting the row and column sub-spaces of gradients. Our algorithms are provably convergent and they achieve the convergence rate of order O(log(T)/√T), where T is the number of iterations. Our experiments illustrate the efficacy of the proposed algorithms on several applications.

本文言語English
ホスト出版物のタイトル36th International Conference on Machine Learning, ICML 2019
出版社International Machine Learning Society (IMLS)
ページ5699-5708
ページ数10
ISBN(電子版)9781510886988
出版ステータスPublished - 2019
外部発表はい
イベント36th International Conference on Machine Learning, ICML 2019 - Long Beach, United States
継続期間: 2019 6 92019 6 15

出版物シリーズ

名前36th International Conference on Machine Learning, ICML 2019
2019-June

Conference

Conference36th International Conference on Machine Learning, ICML 2019
国/地域United States
CityLong Beach
Period19/6/919/6/15

ASJC Scopus subject areas

  • 教育
  • コンピュータ サイエンスの応用
  • 人間とコンピュータの相互作用

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