Optimal Stopping Problem in A Finite State Partially Observable Markov Chain
Tōru Nakai · Journal of Information and Optimization Sciences · 1983
The optimal stopping problem in a Markov chain when there is imperfect state information is considered. Let {Y t , t=1,2, … } denote a n-ary Markov chain with known transition probability matrix. It is assumed that the true state of a chain is not known at time t. Regarding the current state, all the information is summarized by a probability distribution on {1, …, n}. Information regarding the true state of a chain is obtained through a reward process. This problem is formulated as a partially observable Markov decision process. Several properties of the expected value under the optimal policy are developed.