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Geometric convergence of value-iteration in multichain Markov decision problems

Published online by Cambridge University Press:  01 July 2016

P. J. Schweitzer  and
A. Federgruen
P. J. Schweitzer*
Affiliation:
I.B.M. Thomas J. Watson, Research Center
A. Federgruen*
Affiliation:
Mathematisch Centrum, Amsterdam
*
∗Present address: Graduate School of Management, University of Rochester, Rochester, N.Y. 14627, U.S.A.
∗Present address: Graduate School of Management, University of Rochester, Rochester, N.Y. 14627, U.S.A.
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Abstract

This paper considers undiscounted Markov decision problems. With no restriction (on either the periodicity or chain structure of the problem) we show that the value iteration method for finding maximal gain policies exhibits a geometric rate of convergence, whenever convergence occurs. In addition, we study the behaviour of the value-iteration operator; we give bounds for the number of steps needed for contraction, describe the ultimate behaviour of the convergence factor and give conditions for the existence of a uniform convergence rate.

Keywords

MARKOV DECISION PROBLEMSAVERAGE COST CRITERIONVALUE-ITERATION METHODGEOMETRIC CONVERGENCECONVERGENCE FACTOREXISTENCE OF A UNIFORM CONVERGENCE RATE
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 1 , March 1979 , pp. 188 - 217
Copyright
Copyright © Applied Probability Trust 1979 

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