Bayesian Decision Theory Applied to the Finite State Markov Decision Problem
CALIFORNIA UNIV LOS ANGELES SCHOOL OF ENGINEERING AND APPLIED SCIENCE
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Ron Howard solved the Markov decision problem with perfect knowledge of all the transition probabilities and rewards. In a practical situation, the transition probabilities may not be known exactly. Therefore, the problem this research attacks is the Markov decision problem with uncertain transition probabilities. In the case of perfect knowledge, the decision that maximizes the expected reward or gain is chosen. When there is uncertainty in the transition probabilities, the gains become random variables. Therefore, Bayesian decision theory is applied to this problem. A loss function is defined and an a priori density is defined. Bayes formula and the loss function are used to compute a risk for each decision. The decision that minimizes the risk is chosen.
- Operations Research