2017年09月25日 |  English version
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双周三学术报告会:Unified SVRG for Optimization on Riemannian Manifold

报告题目:Unified SVRG for Optimization on Riemannian Manifold

报告人:姜波 博士

时间:2017年4月5日(周三)下午15:00

地点:行健楼学术活动室526

摘要: In this paper, we propose a unified stochastic variance reduced gradient (SVRG) method for empirical risk minimization over Riemannian manifold. Existing SVRG methods on manifold usually consider a specific retraction operation, and involve additional computational costs such as parallel transport or vector transport. The unified SVRG (U-SVRG) we propose in this paper handles general retraction operations, and do not need additional computational costs mentioned above. We analyze the iteration complexity of U-SVRG for obtaining an $\epsilon$-stationary point and its local linear convergence by assuming the \L ojasiewicz inequality, which naturally holds for PCA and holds with high probability for matrix completion problem. Numerical results on PCA and matrix completion problems are reported to demonstrate the efficiency of our methods.

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