Interval Methods for Uncertain Markov Decision Processes

In this paper, the average cases of Markov decision processes with uncertainty is considered. That is, a controlled Markov set-chain model with a finite state and action space is developed by an interval arithmetic analysis, and we will find a Pareto optimal policy which maximizes the average expected rewards over all stationary policies under a new partial order. The Pareto optimal policies is characterized by a maximal solution of an optimality equation which is derived from the model. Also, a maximin policy is obtained and shown to be Pareto-optimal. A numerical example is given.