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Sample-Path Optimal Stationary Policies in Stable Markov Decision Chains with the Average Reward Criterion

Part of: Stochastic systems and control Markov processes

Published online by Cambridge University Press:  30 January 2018

Rolando Cavazos-Cadena ,
Raúl Montes-De-Oca  and
Karel Sladký
Rolando Cavazos-Cadena*
Affiliation:
Universidad Autónoma Agraria Antonio Narro
Raúl Montes-De-Oca*
Affiliation:
Universidad Autónoma Metropolitana-Iztapalapa
Karel Sladký*
Affiliation:
Institute of Information Theory and Automation
*
∗ Postal address: Departamento de Estadística y Cálculo, Universidad Autónoma Agraria Antonio Narro, Buenavista, Saltillo, COAH, 25315, México.Email address: r.cavazoscadena@gmail.com
∗∗ Postal address: Departamento de Matemáticas, Universidad Autónoma Metropolitana, Campus Iztapalapa, Avenida San Rafael Atlixco #186, Colonia Vicentina, México 09340, D. F. México.
∗∗∗ Postal address: Institute of Information Theory and Automation, Pod Vodárenskou věží 4, CZ-182 08, Praha 8, Czech Republic.
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Abstract

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This paper concerns discrete-time Markov decision chains with denumerable state and compact action sets. Besides standard continuity requirements, the main assumption on the model is that it admits a Lyapunov function ℓ. In this context the average reward criterion is analyzed from the sample-path point of view. The main conclusion is that if the expected average reward associated to ℓ2 is finite under any policy then a stationary policy obtained from the optimality equation in the standard way is sample-path average optimal in a strong sense.

Keywords

Dominated convergence theorem for the expected average criteriondiscrepancy functionKolmogorov inequalityinnovationsstrong sample-path optimality

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 93E20: Optimal stochastic control 60J05: Discrete-time Markov processes on general state spaces

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015 , pp. 419 - 440
Copyright
© Applied Probability Trust 

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