  In this paper, a robust optimization framework is developed to train shallow
neural networks based on reachability analysis of neural networks. To
characterize noises of input data, the input training data is disturbed in the
description of interval sets. Interval-based reachability analysis is then
performed for the hidden layer. With the reachability analysis results, a
robust optimization training method is developed in the framework of robust
least-square problems. Then, the developed robust least-square problem is
relaxed to a semidefinite programming problem. It has been shown that the
developed robust learning method can provide better robustness against
perturbations at the price of loss of training accuracy to some extent. At
last, the proposed method is evaluated on a robot arm model learning example.
