图 书 馆
一种用于迹线范数最小化的加速梯度法An Accelerated Gradient Method for Trace Norm Minimization |
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| 课程网址: | http://videolectures.net/icml09_ji_agmt/ |
| 主讲教师: | Shuiwang Ji |
| 开课单位: | 华盛顿州立大学 |
| 开课时间: | 2009-08-26 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | We consider the minimization of a smooth loss function regularized by the trace norm of the matrix variable. Such formulation finds applications in many machine learning tasks including multi-task learning, matrix classification, and matrix completion. The standard semidefinite programming formulation for this problem is computationally expensive. In addition, due to the non-smoothness nature of the trace norm, the optimal first-order black-box method for solving such class of problems converges as O(1/sqrt(k)), where k is the iteration counter. In this paper, we exploit the special structure of the trace norm, based on which we propose an extended gradient algorithm that converges as O(1/k). We further propose an accelerated gradient algorithm, which achieves the optimal convergence rate of O(1/k^2) for smooth problems. Experiments on multi-task learning problems demonstrate the efficiency of the proposed algorithms. |
| 关 键 词: | 矩阵变量; 平滑损失函数; 跟踪范数 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-04-23：lxf |
| 阅读次数: | 159 |