Existence of optimal policies for semi-markov decision processes using duality for infinite linear programming

Diego Klabjan*, Daniel Adelman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

Semi-Markov decision processes on Borel spaces with deterministic kernels have many practical applications, particularly in inventory theory. Most of the results from general semi-Markov decision processes do not carry over to a deterministic kernel since such a kernel does not provide "smoothness. " We develop infinite dimensional linear programming theory for a general stochastic semi-Markov decision process. We give conditions, general enough to allow deterministic kernels, for solvability and strong duality of the resulting linear programs. By using the developed linear programming theory we give conditions for the existence of a stationary deterministic policy for deterministic kernels, which is optimal among all possible policies.

Original languageEnglish (US)
Pages (from-to)2104-2122
Number of pages19
JournalSIAM Journal on Control and Optimization
Volume44
Issue number6
DOIs
StatePublished - Jan 2006

Keywords

  • Linear programming
  • Optimal policies
  • Semi-Markov decision processes

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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