Risk-averting criteria for training neural networks

This paper shows that when a risk-averting error criterion is used to train a neural network or estimate a nonlinear regression model, as the risk-sensitivity index of the criterion increases. the domain on which the criterion is convex increases monotonically to the entire weight or parameter vector space R-N except the union of a finite number of manifolds whose dimensions are less than N. This paper also shows that inreasing the risk-sensitivity index reduces the maximum deviation of the outputs of the trained neural network or estimated regression model from the corresponding output measurements.