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Computable approximations for average Markov decision processes in continuous time

Published online by Cambridge University Press:  26 July 2018

Jonatha Anselmi ,
François Dufour  and
Tomás Prieto-Rumeau
Jonatha Anselmi*
Affiliation:
INRIA
François Dufour*
Affiliation:
INRIA and Université de Bordeaux
Tomás Prieto-Rumeau*
Affiliation:
UNED
*
* Postal address: INRIA Bordeaux Sud Ouest, Bureau B430, 200 av. de la Vieille Tour, 33405 Talence cedex, France. Email address: [email protected]
** Postal address: Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351 cours de la Libération, F33405 Talence, France. Email address: [email protected]
*** Postal address: Statistics Department, UNED, calle Senda del Rey 9, 28040 Madrid, Spain. Email address: [email protected]
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Abstract

In this paper we study the numerical approximation of the optimal long-run average cost of a continuous-time Markov decision process, with Borel state and action spaces, and with bounded transition and reward rates. Our approach uses a suitable discretization of the state and action spaces to approximate the original control model. The approximation error for the optimal average reward is then bounded by a linear combination of coefficients related to the discretization of the state and action spaces, namely, the Wasserstein distance between an underlying probability measure μ and a measure with finite support, and the Hausdorff distance between the original and the discretized actions sets. When approximating μ with its empirical probability measure we obtain convergence in probability at an exponential rate. An application to a queueing system is presented.

Keywords

Continuous-time Markov decision processLipschitz continuous control modelapproximation of the optimal value function

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 90C39: Dynamic programming
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 2 , June 2018 , pp. 571 - 592
Copyright
Copyright © Applied Probability Trust 2018 

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References

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