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Mar, 2024
鲁棒二阶非凸优化及其在低秩矩阵感知中的应用
Robust Second-Order Nonconvex Optimization and Its Application to Low Rank Matrix Sensing
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Shuyao Li, Yu Cheng, Ilias Diakonikolas, Jelena Diakonikolas, Rong Ge...
TL;DR
使用强污染模型的泛用框架,以高效且可靠的算法逼近具有维度无关的精度保证的二阶稳定点,可应用于含异常值的优化问题,特别在低秩矩阵感知中表现出鲁棒性,并证明了样本复杂性与维度存在二次依赖关系的统计查询下界。
Abstract
Finding an
approximate second-order stationary point
(SOSP) is a well-studied and fundamental problem in
stochastic nonconvex optimization
with many applications in machine learning. However, this problem is poor
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