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Optimal decision procedures for finite markov chains. Part I: Examples

Published online by Cambridge University Press:  01 July 2016

John Bather
John Bather*
Affiliation:
University of Sussex
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Abstract

A Markov process in discrete time with a finite state space is controlled by choosing the transition probabilities from a prescribed set depending on the state occupied at any time. Given the immediate cost for each choice, it is required to minimise the expected cost over an infinite future, without discounting. Various techniques are reviewed for the case when there is a finite set of possible transition matrices and an example is given to illustrate the unpredictable behaviour of policy sequences derived by backward induction. Further examples show that the existing methods may break down when there is an infinite family of transition matrices. A new approach is suggested, based on the idea of classifying the states according to their accessibility from one another.

Keywords

MARKOV CHAINDECISION PROCEDUREMINIMUM AVERAGE COSTOPTIMAL POLICYHOWARD MODELDYNAMIC PROGRAMMINGCONVEX DECISION SPACEACCESSIBILITY
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 2 , August 1973 , pp. 328 - 339
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Blackwell, D. (1962) Discrete dynamic programming. Ann. Math. Statist. 33, 719–726.CrossRefGoogle Scholar
[2] Brown, B. W. (1965) On the iterative method of dynamic programming on a finite space discrete time Markov process. Ann. Math. Statist. 36, 1279–1286.CrossRefGoogle Scholar
[3] Derman, C. (1970) Finite State Markovian Decision Processes. Academic Press, New York.Google Scholar
[4] Howard, R. A. (1960) Dynamic Programming and Markov Processes. Wiley, New York.Google Scholar
[5] Kemeny, J. G. and Snell, J. L. (1960) Finite Markov Chains. Van Nostrand, New York.Google Scholar
[6] Lanery, E. (1967) Étude asymptotique des systèmes Markoviens à commande. Revue d'Informatique et Recherche Opérationnelle. 1 no. 6, 3–56.Google Scholar
[7] Miller, B. L. and Veinott, A. F. Jr. (1969) Discrete dynamic programming with a small interest rate. Ann. Math. Statist. 40, 366–370.CrossRefGoogle Scholar
[8] Veinott, A. F. Jr. (1966) On finding optimal policies in discrete dynamic programming with no discounting. Ann. Math. Statist. 37, 1284–1294.CrossRefGoogle Scholar
[9] Veinott, A. F. Jr. (1969) Discrete dynamic programming with sensitive discount optimality criteria. Ann. Math. Statist. 40, 1635–1660.CrossRefGoogle Scholar