Some Monotonicity Results for Partially Observed Markov Decision Processes

This paper provides sufficient conditions for the optimal value in a discrete-time, finite, partially observed Markov decision process to be monotone on the space of state probability vectors ordered by likelihood ratios. The paper also presents sufficient conditions for the optimal policy to be monotone in a simple machine replacement problem, and, in the general case, for the optimal policy to be bounded from below by an easily calculated monotone function.