Title: Second-Order Optimization for Non-Convex Machine Learning: An Empirical Study,
Abstract: While first-order optimization methods such as stochastic gradient descent
(SGD) are popular in machine learning (ML), they come with well-known
deficiencies, including relatively-slow convergence, sensitivity to the
settings of hyper-parameters such as learning rate, stagnation at high training
errors, and difficulty in escaping flat regions and saddle points. These issues
are particularly acute in highly non-convex settings such as those arising in
neural networks. Motivated by this, there has been recent interest in
second-order methods that aim to alleviate these shortcomings by capturing
curvature information. In this paper, we report detailed empirical evaluations
of a class of Newton-type methods, namely sub-sampled variants of trust region
(TR) and adaptive regularization with cubics (ARC) algorithms, for non-convex
ML problems. In doing so, we demonstrate that these methods not only can be
computationally competitive with hand-tuned SGD with momentum, obtaining
comparable or better generalization performance, but also they are highly
robust to hyper-parameter settings. Further, in contrast to SGD with momentum,
we show that the manner in which these Newton-type methods employ curvature
information allows them to seamlessly escape flat regions and saddle points.