76 citations · 76 across the 1 of their papers we have counts for
3 papers
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…
Best-of-K Bandits
Max Simchowitz, Kevin Jamieson, Benjamin Recht
This paper studies the Best-of-K Bandit game: At each time the player chooses a subset S among all N-choose-K possible options and observes reward max(X(i) : i in S) where X is a r…
Gradient Descent Converges to Minimizers
Jason D. Lee, Max Simchowitz, Michael I. Jordan +1
We show that gradient descent converges to a local minimizer, almost surely with random initialization. This is proved by applying the Stable Manifold Theorem from dynamical system…