Constrained total undiscounted continuous-time Markov decision processes

Xianping Guo, Yi Zhang

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

The present paper considers the constrained optimal control problem with total undiscounted criteria for a continuous-time Markov decision process (CTMDP) in Borel state and action spaces. The cost rates are nonnegative. Under the standard compactness and continuity conditions, we show the existence of an optimal stationary policy out of the class of general nonstationary ones. In the process, we justify the reduction of the CTMDP model to a discrete-time Markov decision process (DTMDP) model based on the studies of the undiscounted occupancy and occupation measures. We allow that the controlled process is not necessarily absorbing, and the transition rates are not necessarily separated from zero, and can be arbitrarily unbounded; these features count for the main technical difficulties in studying undiscounted CTMDP models.

Original languageEnglish
Pages (from-to)1694-1736
Number of pages43
JournalBernoulli
Volume23
Issue number3
DOIs
Publication statusPublished - Aug 2017

Keywords

  • Constrained optimality
  • Continuous-time Markov decision processes
  • Total undiscounted criteria

ASJC Scopus subject areas

  • Statistics and Probability

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