论文标题
加速核电 - 正规化低级矩阵通过Burer-Monteiro分解
Accelerating nuclear-norm regularized low-rank matrix optimization through Burer-Monteiro decomposition
论文作者
论文摘要
这项工作提出了一种快速的算法BM-Global，用于核合作调节式凸和低级别基质优化问题。 BM-Global efficiently decreases the objective value via low-cost steps leveraging the nonconvex but smooth Burer-Monteiro (BM) decomposition, while effectively escapes saddle points and spurious local minima ubiquitous in the BM form to obtain guarantees of fast convergence rates to the global optima of the original nuclear-norm-regularized problem through aperiodic inexact proximal gradient steps on it.所提出的方法适应地调整了BM分解的等级，并可以通过多种识别工具在优化过程中自动确定BM分解问题的最佳等级。因此，BM-Global在参数调整上花费的时间比现有矩阵 - 归化方法的时间要少得多，这需要详尽地搜索找到此最佳等级。对现实世界中建议系统的大规模问题，正则化核的估计和分子构象的广泛实验证实，BM-Global确实可以有效地逃脱出虚假的局部最小值，而现有的BM方法被卡住了，并且比不可能的较低的ARGORITH量更快地涉及较低的Argithms，该算法涉及低级基质的涉及型核核酸的低位核心。基于这项研究，我们在https://www.github.com/leepei/bm-global/上发布了拟议的BM-Global的开源包。
This work proposes a rapid algorithm, BM-Global, for nuclear-norm-regularized convex and low-rank matrix optimization problems. BM-Global efficiently decreases the objective value via low-cost steps leveraging the nonconvex but smooth Burer-Monteiro (BM) decomposition, while effectively escapes saddle points and spurious local minima ubiquitous in the BM form to obtain guarantees of fast convergence rates to the global optima of the original nuclear-norm-regularized problem through aperiodic inexact proximal gradient steps on it. The proposed approach adaptively adjusts the rank for the BM decomposition and can provably identify an optimal rank for the BM decomposition problem automatically in the course of optimization through tools of manifold identification. BM-Global hence also spends significantly less time on parameter tuning than existing matrix-factorization methods, which require an exhaustive search for finding this optimal rank. Extensive experiments on real-world large-scale problems of recommendation systems, regularized kernel estimation, and molecular conformation confirm that BM-Global can indeed effectively escapes spurious local minima at which existing BM approaches are stuck, and is a magnitude faster than state-of-the-art algorithms for low-rank matrix optimization problems involving a nuclear-norm regularizer. Based on this research, we have released an open-source package of the proposed BM-Global at https://www.github.com/leepei/BM-Global/.
