Publicación: Absorbing Markov decision processes
Fecha
2024-02-09
Autores
Dufour, François
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info:eu-repo/semantics/openAccess
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EDP Sciences
Resumen
In this paper, we study discrete-time absorbing Markov Decision Processes (MDP) with measurable state space and Borel action space with a given initial distribution. For such models, solutions to the characteristic equation that are not occupation measures may exist. Several necessary and sufficient conditions are provided to guarantee that any solution to the characteristic equation is an occupation measure. Under the so-called continuity-compactness conditions, we first show that a measure is precisely an occupation measure if and only if it satisfies the characteristic equation and an additional absolute continuity condition. Secondly, it is shown that the set of occupation measures is compact in the weak-strong topology if and only if the model is uniformly absorbing. Several examples are provided to illustrate our results.
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Categorías UNESCO
Palabras clave
Markov decision processes, absorbing model, occupation measures, characteristic equation, phantom measures, compactness of the set of occupation measures
Citación
Absorbing Markov decision processes. François Dufour, Tomás Prieto-Rumeau. ESAIM: COCV 30 5 (2024) https://www.esaim-cocv.org/articles/cocv/abs/2024/01/cocv230200/cocv230200.html https://doi.org/10.1051/cocv/2024002
Centro
Facultades y escuelas::Facultad de Ciencias
Departamento
Estadística, Investigación Operativa y Cálculo Numérico