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.
|出版ステータス||Published - 2018|
|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 9 → 2018 4月 11
|Conference||21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018|
|City||Playa Blanca, Lanzarote, Canary Islands|
|Period||18/4/9 → 18/4/11|
ASJC Scopus subject areas