Markov Decision Processes with Incomplete Information and Semi-Uniform Feller Transition Probabilities

Abstract: This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semi-uniform Feller transition probabilities. The important feature of these models is that their classic reduction to Completely Observable Markov Decision Processes with belief states preserves semi-uniform Feller continuity of transition probabilities. Under mild assumptions on cost functions, optimal policies exist, optimality equations hold, and value iterations converge to optimal values for these models. In particular, for Partially Observable Markov Decision Processes the results of this paper imply new and generalize several known sufficient conditions on transition and observation probabilities for weak continuity of transition probabilities for Markov Decision Processes with belief states, the existence of optimal policies, validity of optimality equations defining optimal policies, and convergence of value iterations to optimal values.