The normalized risk-averting error criterion for avoiding nonglobal local minima in training neural networks.

The convexification method for data fitting is capable of avoiding nonglobal local minima, but suffers from two shortcomings: the risk-averting error (RAE) criterion grows exponentially as its risk-sensitivity index λ increases, and the existing method of determining λ is often not effective. To eliminate these shortcomings, the normalized RAE (NRAE) is herein proposed. As NRAE is a monotone increasing function of RAE, the region without a nonglobal local minimum of NRAE expands as does that of RAE. However, NRAE does not grow unboundedly as does RAE.