Inertial Newton Algorithms Avoiding Strict Saddle Points

Abstract

We study the asymptotic behavior of second-order algorithms mixing Newton's method and inertial gradient descent in non-convex landscapes. We show that, despite the Newtonian behavior of these methods, they almost always escape strict saddle points. We also evidence the role played by the hyper-parameters of these methods in their qualitative behavior near critical points. The theoretical results are supported by numerical illustrations.

References in corpus (3)

• The NumPy array: a structure for efficient numerical computation
• Identifying and attacking the saddle point problem in high-dimensional non-convex optimization
• First order optimization methods based on Hessian-driven Nesterov accelerated gradient flow