A reinforcement learning neural network for adaptive control of Markov chains

In this paper we consider the problem of reinforcement learning in a dynamically changing environment. In this context, we study the problem of adaptive control of finite-state Markov chains with a finite number of controls. The transition and payoff structures are unknown. The objective is to find an optimal policy which maximizes the expected total discounted payoff over the infinite horizon. A stochastic neural network model is suggested for the controller. The parameters of the neural net, which determine a random control strategy, are updated at each instant using a simple learning scheme. This learning scheme involves estimation of some relevant parameters using an adaptive critic. It is proved that the controller asymptotically chooses an optimal action in each state of the Markov chain with a high probability.