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Optimality conditions for a Markov decision chain with unbounded costs

Published online by Cambridge University Press:  14 July 2016

D. R. Robinson
D. R. Robinson*
Affiliation:
University of Manchester
*
∗Postal address: Statistical Laboratory, Department of Mathematics, The University, Manchester M13 9PL, U.K.
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Abstract

It is known that when costs are unbounded satisfaction of the appropriate dynamic programming ‘optimality' equation by a policy is not sufficient to guarantee its average optimality. A ‘lowest-order potential' condition is introduced which, along with the dynamic programming equation, is sufficient to establish the optimality of the policy. Also, it is shown that under fairly general conditions, if the lowest-order potential condition is not satisfied there exists a non-memoryless policy with smaller average cost than the policy satisfying the dynamic programming equation.

Keywords

MARKOV DECISION CHAINUNBOUNDED ONE-STEP COSTSOPTIMALITY EQUATIONDYNAMIC PROGRAMMING
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 996 - 1003
Copyright
Copyright © Applied Probability Trust 

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