@article{Huang_Liang_Liu_Li_Yu_Li_2020, title={SPAN: A Stochastic Projected Approximate Newton Method}, volume={34}, url={https://ojs.aaai.org/index.php/AAAI/article/view/5511}, DOI={10.1609/aaai.v34i02.5511}, abstractNote={<p>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.</p>}, number={02}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Huang, Xunpeng and Liang, Xianfeng and Liu, Zhengyang and Li, Lei and Yu, Yue and Li, Yitan}, year={2020}, month={Apr.}, pages={1520-1527} }