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May, 2016
低秩矩阵恢复的局部搜索的全局最优性
Global Optimality of Local Search for Low Rank Matrix Recovery
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Srinadh Bhojanapalli, Behnam Neyshabur, Nathan Srebro
TL;DR
该研究表明，使用非凸因式分解的参数化方法可以从不一致的线性测量中恢复低秩矩阵，且不存在虚假的局部最小值。并且在有噪声的测量中，所有局部最小值都非常靠近全局最优解。结合鞍点的曲率界限，保证了随机梯度下降从随机初始化出发以多项式时间全局收敛。
Abstract
We show that there are no spurious local minima in the
non-convex factorized parametrization
of
low-rank matrix recovery
from incoherent linear measurements. With noisy measurements we show all local minima are v
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