Application of Reinforcement Learning Algorithms for the Adaptive Computation of the Smoothing Parameter for Probabilistic Neural Network

In this paper, we propose new methods for the choice and adaptation of the smoothing parameter of the probabilistic neural network (PNN). These methods are based on three reinforcement learning algorithms: Q(0)-learning, Q(λ)-learning, and stateless Q-learning. We regard three types of PNN classifiers: the model that uses single smoothing parameter for the whole network, the model that utilizes single smoothing parameter for each data attribute, and the model that possesses the matrix of smoothing parameters different for each data variable and data class. Reinforcement learning is applied as the method of finding such a value of the smoothing parameter, which ensures the maximization of the prediction ability. PNN models with smoothing parameters computed according to the proposed algorithms are tested on eight databases by calculating the test error with the use of the cross validation procedure. The results are compared with state-of-the-art methods for PNN training published in the literature up to date and, additionally, with PNN whose sigma is determined by means of the conjugate gradient approach. The results demonstrate that the proposed approaches can be used as alternative PNN training procedures.