FIT2016 第15回情報科学技術フォーラム 開催日:2016年9月7日(水)~9日(金) 会場:富山大学キャンパス
Riemannian stochastic variance reduced gradient on Grassmann manifold
Hiroyuki Kasai(The Univ. of Electro-Communications)・Hiroyuki Sato(Tokyo Univ. of Science)・Bamdev Mishra(Amazon Development Centre India)
In this paper, we propose a novel Riemannian extension of the Euclidean stochastic variance reduced gradient algorithm to a compact manifold search space. To this end, we show the developments on the Grassmann manifold. We present a global convergence analysis of the proposed algorithm with a decay step-size and a local convergence rate analysis under a fixed step-size with under some natural assumptions. The proposed algorithm is applied on a number of problems on the Grassmann manifold. In all these cases, the proposed algorithm outperforms the standard Riemannian stochastic gradient descent algorithm.