论文标题
塔克分解的优化景观
Optimization Landscape of Tucker Decomposition
论文作者
论文摘要
塔克分解是许多数据分析和机器学习应用程序的流行技术。找到塔克分解是一个非convex优化问题。随着问题的规模的增加，本地搜索算法（如随机梯度下降）在实践中变得流行。在本文中，我们表征了塔克分解问题的优化格局。特别是，我们表明，如果张量具有精确的塔克分解，对于塔克分解的标准非凸目标，所有局部最小值也是全球最佳的。我们还提供了一种本地搜索算法，该算法可以在多项式时间内找到近似的局部（和全局）最佳解决方案。
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.
