The Optimal Observability of Partially Observable Markov Decision Processes: Discrete State Space

We consider autonomous partially observable Markov decision processes where the control action influences the observation process only. Considering entropy as the cost incurred by the Markov information state process, the optimal observability problem is posed as a Markov decision scheduling problem that minimizes the infinite horizon cost. This scheduling problem is shown to be equivalent to minimization of an entropy measure, called estimation entropy which is related to the invariant measure of the information state.