论文标题
基于近端操作员及其在公制学习中的应用程序的Riemannian原始二线算法
A Riemannian Primal-dual Algorithm Based on Proximal Operator and its Application in Metric Learning
论文作者
论文摘要
在本文中，我们考虑优化带有约束的Riemannian空间中平滑，较低的半连续功能。为了解决该问题，我们首先将其转换为双重问题，然后提出一种一般的原始偶对算法，以优化原始变量和双重变量。在每次优化迭代中，我们使用近端操作员在原始空间中搜索最佳解决方案。我们证明了所提出的算法的收敛性，并显示其非质子收敛速率。通过利用所提出的原始二重式优化技术，我们提出了一种新型的度量学习算法，该算法在Riemannian空间中学习了一个正定确定矩阵的最佳特征转换矩阵。基金管理基金（FOF）管理中的最佳基金选择问题的初步实验结果显示了其功效。
In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to optimize the primal and dual variables iteratively. In each optimization iteration, we employ a proximal operator to search optimal solution in the primal space. We prove convergence of the proposed algorithm and show its non-asymptotic convergence rate. By utilizing the proposed primal-dual optimization technique, we propose a novel metric learning algorithm which learns an optimal feature transformation matrix in the Riemannian space of positive definite matrices. Preliminary experimental results on an optimal fund selection problem in fund of funds (FOF) management for quantitative investment showed its efficacy.
