Statistical Mechanics of On-line Node-perturbation Learning

Node-perturbation learning (NP-learning) is a kind of statistical gradient descent algorithm that estimates the gradient of an objective function through application of a small perturbation to the outputs of the network. It can be applied to problems where the objective function is not explicitly formulated, including reinforcement learning. In this paper, we show that node-perturbation learning can be formulated as on-line learning in a linear perceptron with noise, and we can derive the differential equations of order parameters and the generalization error in the same way as for the analysis of learning in a linear perceptron through statistical mechanical methods. From analytical results, we show that cross-talk noise, which originates in the error of the other outputs, increases the generalization error as the output number increases.