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Optimal stopping model with unknown transition probabilities

Horiguchi M., Piunovskiy A. B.

Control and Cybernetics

2013

Vol. 42, no. 3

593--612

This article concerns the optimal stopping problem for a discrete-time Markov chain with observable states, but with unknown transition probabilities. A stopping policy is graded via the expected total-cost criterion resulting from the non-negative running and terminal costs. The Dynamic Programming method, combined with the Bayesian approach, is developed. A series of explicitly solved meaningful examples illustrates all the theoretical issues.

Dynamic programming in constrained Markov decision

Piunovskiy A. B.

Control and Cybernetics

2006

Vol. 35, no 3

645-660

We consider a discounted Markov Decision Process (MDP) supplemented with the requirement that another discounted loss must not exceed a specified value, almost surely. We show that he problem can be reformulated as a standard MDP and solved using the Dynamic Programming approach. An example on a controlled queue is presented. In the last section, we briefly reinforce the connection of the Dynamic Programming approach to another close problem statement and present the corresponding example. Several other types of constraints are discussed, as well.