Structural Results for Partially Observable Markov Decision Processes

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Abstract
This paper examines monotonicity results for a fairly general class of partially observable Markov decision processes. When there are only two actual states in the system and when the actions taken are primarily intended to improve the system, rather than to inspect it, we give reasonable conditions which ensure that the optimal reward function and the optimal action are both monotone in the current state of information. Examples of maintenance systems and advertising systems for which our results hold are given. Finally, we examine the case where there are three or more actual states and indicate the difficulties encountered when we attempt to extend the monotonicity results to this situation.

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