Saddle-free Hessian-free Optimization

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.