229 citations · 664 across the 18 of their papers we have counts for
4 papers · 1 filter
Stochastic Cubic Regularization for Fast Nonconvex Optimization
Nilesh Tripuraneni, Mitchell Stern, Chi Jin +2
This paper proposes a stochastic variant of a classic algorithm---the cubic-regularized Newton method [Nesterov and Polyak 2006]. The proposed algorithm efficiently escapes saddle…
Accelerated Gradient Descent Escapes Saddle Points Faster than Gradient Descent
Chi Jin, Praneeth Netrapalli, Michael I. Jordan
Nesterov's accelerated gradient descent (AGD), an instance of the general family of "momentum methods", provably achieves faster convergence rate than gradient descent (GD) in the…
Gradient Descent Can Take Exponential Time to Escape Saddle Points
Simon S. Du, Chi Jin, Jason D. Lee +3
Although gradient descent (GD) almost always escapes saddle points asymptotically [Lee et al., 2016], this paper shows that even with fairly natural random initialization schemes a…
How to Escape Saddle Points Efficiently
Chi Jin, Rong Ge, Praneeth Netrapalli +2
This paper shows that a perturbed form of gradient descent converges to a second-order stationary point in a number iterations which depends only poly-logarithmically on dimension…