Recurrent neural networks training with stable risk-sensitive Kalman filter algorithm

Compared to normal learning algorithms, for example backpropagation, Kalman filter-based algorithm has some better properties, such as faster convergence. In this paper, Kalman filter is modified with a risk-sensitive cost criterion, we call it as risk-sensitive Kalman filter. This new algorithm is applied to train recurrent neural networks for nonlinear system identification. Input-to-state stability is used to prove that the risk-sensitive Kalman filter training is stable. The contributions of this paper are: 1) the risk-sensitive Kalman filter is used for the state-space recurrent neural networks training, 2) the stability of the risk-sensitive Kalman filter is proved.