Algorithms for solving optimization problems arising from deep neural net models: smooth problems

TL;DR

This paper discusses optimization algorithms for complex nonlinear problems in deep neural networks, highlighting a Newton-based method with negative curvature directions and demonstrating promising results in security anomaly detection.

Contribution

It introduces a Newton-based optimization approach incorporating negative curvature directions for deep neural network training problems.

Findings

Effective in security anomaly detection datasets

Shows promising numerical results

Addresses challenges of nonlinear optimization in deep learning

Abstract

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the empirical risk is, however, highly nonlinear. This presents a challenge to application and development of appropriate optimization algorithms for solving the problem. In this paper, we summarize the primary challenges involved and present the case for a Newton-based method incorporating directions of negative curvature, including promising numerical results on data arising from security anomally deetection.