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Optimization Landscape of Tucker Decomposition
arXiv - CS - Machine Learning Pub Date : 2020-06-29 , DOI: arxiv-2006.16297
Abraham Frandsen, Rong Ge

Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such as stochastic gradient descent have become popular in practice. In this paper, we characterize the optimization landscape of the Tucker decomposition problem. In particular, we show that if the tensor has an exact Tucker decomposition, for a standard nonconvex objective of Tucker decomposition, all local minima are also globally optimal. We also give a local search algorithm that can find an approximate local (and global) optimal solution in polynomial time.

中文翻译:

Tucker 分解的优化图景

Tucker 分解是许多数据分析和机器学习应用程序的流行技术。寻找 Tucker 分解是一个非凸优化问题。随着问题规模的增加,随机梯度下降等局部搜索算法在实践中变得流行起来。在本文中,我们描述了 Tucker 分解问题的优化前景。特别是,我们表明,如果张量具有精确的 Tucker 分解,则对于 Tucker 分解的标准非凸目标,所有局部最小值也是全局最优的。我们还给出了一种局部搜索算法,可以在多项式时间内找到近似的局部(和全局)最优解。
更新日期:2020-07-01
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