Saddle-free Hessian-free Optimization
This work addresses a key bottleneck in training deep neural networks by making second-order methods more practical, which could improve optimization efficiency for researchers and practitioners.
The paper tackles the problem of saddle point proliferation in nonconvex optimization for deep learning by introducing a novel algorithm that addresses computational complexity and avoidance of high-error saddle points, enabling the application of Newton's method advantages in high-dimensional settings.
Nonconvex optimization problems such as the ones in training deep neural networks suffer from a phenomenon called saddle point proliferation. This means that there are a vast number of high error saddle points present in the loss function. Second order methods have been tremendously successful and widely adopted in the convex optimization community, while their usefulness in deep learning remains limited. This is due to two problems: computational complexity and the methods being driven towards the high error saddle points. We introduce a novel algorithm specially designed to solve these two issues, providing a crucial first step to take the widely known advantages of Newton's method to the nonconvex optimization community, especially in high dimensional settings.