137 citations · 419 across the 10 of their papers we have counts for
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stat.ML2017★ 76 cited
First-order Methods Almost Always Avoid Saddle Points
Jason D. Lee, Ioannis Panageas, Georgios Piliouras +3
We establish that first-order methods avoid saddle points for almost all initializations. Our results apply to a wide variety of first-order methods, including gradient descent, bl…
cs.LG2017★ 7 cited
On the Gap Between Strict-Saddles and True Convexity: An Omega(log d) Lower Bound for Eigenvector Approximation
Max Simchowitz, Ahmed El Alaoui, Benjamin Recht
We prove a \emph{query complexity} lower bound on rank-one principal component analysis (PCA). We consider an oracle model where, given a symmetric matrix $M \in \mathbb{R}^{d \tim…