Tucker分解是許多資料分析和機器學習應用中的一種流行技術。尋找塔克分解是一個非凸優化問題。随着問題規模的增大，随機梯度下降等局部搜尋算法在實際中得到了廣泛的應用。本文刻畫了Tucker分解問題的優化圖景。特别地，我們證明了如果張量具有精确的Tucker分解，對于Tucker分解的标準非凸目标，所有局部極小值也是全局最優的。我們還提出了一種局部搜尋算法，可以在多項式時間内找到近似的局部（和全局）最優解。
原文題目：Optimization Landscape of Tucker Decomposition
原文作者：Abraham Frandsen, Rong Ge
原文：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.
原文位址：https://arxiv.org/abs/2006.16297
Optimization Landscape of Tucker Decomposition.pdf