Review of second-order optimization techniques in artificial neural networks backpropagation

Second-order optimization technique is the advances of first-order optimization in neural networks. It provides an addition curvature information of an objective function that adaptively estimate the step-length of optimization trajectory in training phase of neural network. With the additional information, it reduces training iteration and achieves fast convergence with less tuning of hyper-parameter. The current improved memory allocation and computing power further motivates machine learning practitioners to revisit the benefits of second-order optimization techniques. This paper covers the review on second-order optimization techniques that involve Hessian calculation for neural network training. It reviews the basic theory of Newton method, quasi-Newton, Gauss-Newton, Levenberg-Marquardt, Approximate Greatest Descent and Hessian-Free optimization. This paper summarizes the feasibility and performance of optimization techniques in deep neural network training. Comments and suggestions are highlighted for second-order optimization techniques in artificial neural network training in term of advantages and limitations.