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Detecting optimal and non-optimal actions in average-cost Markov decision processes

Part of: Markov processes Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Jean B. Lasserre
Jean B. Lasserre*
Affiliation:
LAAS-CNRS
*
∗Postal address: LAAS-CNRS, 7 Av. Colonel Roche, 31 077 Toulouse Cedex, France.
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Abstract

We present two sufficient conditions for detection of optimal and non-optimal actions in (ergodic) average-cost MDPs. They are easily interpreted and can be implemented as detection tests in both policy iteration and linear programming methods. An efficient implementation of a recent new policy iteration scheme is discussed.

Keywords

POLICY ITERATIONLINEAR PROGRAMMINGELIMINATION OF NON-OPTIMAL ACTIONS

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 93E20: Optimal stochastic control 90C40: Markov and semi-Markov decision processes
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 979 - 990
Copyright
Copyright © Applied Probability Trust 1994 

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References

[1] Bean, J., Hopp, W. and Duenyas, I. (1993) A stopping rule for forecast horizons in nonhomogeneous Markov decision processes. Operat. Res. 40, 1188–1199.Google Scholar
[2] Bes, C. and Lasserre, J. B. (1986) An on-line procedure in discounted infinite horizon stochastic optimal control. J. Optim. Theory Appl. 50, 61–67.Google Scholar
[3] Cheng, M. C. (1980) New criteria for the simplex algorithm. Math. Progr. 19, 230–236.Google Scholar
[4] Denardo, E. V. and Fox, B. (1968) Multichain renewal programs. SIAM J. Appl. Math. 16, 468–487.Google Scholar
[5] Hastings, N. A. J. (1976) A test for non-optimal actions in undiscounted finite Markov decision chains. Management Sci. 23, 87–92.CrossRefGoogle Scholar
[6] Howard, R. (1960) Dynamic Programming and Markov Processes. MIT Press, Cambridge, MA.Google Scholar
[7] Kallenberg, L. M. C. (1983) Linear Programming and Finite Markovian Control Problems. Mathematical Centre Tracts, Mathematisch Centrum. Amsterdam.Google Scholar
[8] Lasserre, J. B. (1994) A new policy iteration scheme for Markov decision processes using Schweitzer's formula. J. Appl. Prob. 31, 268–273.Google Scholar
[9] Puterman, M. (1990) Markov decision processes. In Handbook in Operations Research and Management Science 2: Stochastic Models , ed. Heyman, D. P. and Sobel, M., North-Holland, Amsterdam.Google Scholar
[10] Van Der Wal, J. (1976) A successive approximation algorithm. Computing 17, 157–162.Google Scholar