F-008
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.