SPAN: A Stochastic Projected Approximate Newton Method

• URL: http://arxiv.org/abs/2002.03687v2
• Date: Tue, 3 Mar 2020 02:01:33 GMT
• Title: SPAN: A Stochastic Projected Approximate Newton Method
• Authors: Xunpeng Huang, Xianfeng Liang, Zhengyang Liu, Yitan Li, Linyun Yu, Yue Yu, Lei Li
• Abstract summary: We propose SPAN, a novel approximate and fast Newton method to compute the inverse of the Hessian matrix. SPAN outperforms existing first-order and second-order optimization methods in terms of the convergence wall-clock time.
• Score: 17.94221425332409
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Second-order optimization methods have desirable convergence properties. However, the exact Newton method requires expensive computation for the Hessian and its inverse. In this paper, we propose SPAN, a novel approximate and fast Newton method. SPAN computes the inverse of the Hessian matrix via low-rank approximation and stochastic Hessian-vector products. Our experiments on multiple benchmark datasets demonstrate that SPAN outperforms existing first-order and second-order optimization methods in terms of the convergence wall-clock time. Furthermore, we provide a theoretical analysis of the per-iteration complexity, the approximation error, and the convergence rate. Both the theoretical analysis and experimental results show that our proposed method achieves a better trade-off between the convergence rate and the per-iteration efficiency.

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