Some advances on constrained Markov decision processes in Borel spaces with random state-dependent discount factors

Héctor Jasso-Fuentes, Raquiel R. López-Martínez, J. Adolfo Minjárez-Sosa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper addresses a class of discrete-time Markov decision processes in Borel spaces with a finite number of cost constraints. The constrained control model considers costs of discounted type with state-dependent discount factors which are subject to external disturbances. Our objective is to prove the existence of optimal control policies and characterize them according to certain optimality criteria. Specifically, by rewriting appropriately our original constrained problem as a new one on a space of occupation measures, we apply the direct method to show solvability. Next, the problem is defined as a convex program, and we prove that the existence of a saddle point of the associated Lagrangian operator is equivalent to the existence of an optimal control policy for the constrained problem. Finally, we turn our attention to multi-objective optimization problems, where the existence of Pareto optimal policies can be obtained from the existence of saddle-points of the aforementioned Lagrangian or equivalently from the existence of optimal control policies of constrained problems.

Original languageEnglish
JournalOptimization
DOIs
StateAccepted/In press - 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • 90C40
  • 93E20
  • constrained control problems
  • convex programming
  • Markov decision processes
  • Pareto optimality
  • random non-constant discount factor

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