On the existence of relative values for undiscounted Markovian decision processes with a scalar gain rate
type: Item
instance of: scholarly article
title: On the existence of relative values for undiscounted Markovian decision processes with a scalar gain rate
zbMATH Open document ID: 0598.90091
DOI: 10.1016/0022-247X(84)90031-3
author: Paul J. Schweitzer
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: The functional equations \(v=\max \{q(f)-gT(f)+P(f)v\); \(f\in K\}\equiv Qv\) of undiscounted semi-Markovian decision processes are shown to be solvable if and only if all components of the maximum gain rate vector are equal. More generally, in the multichain case, the functional equations for the value vector possess a solution if and only if there is a policy which achieves the maximal gain vector. The method of proof exhibits vectors \(v^{\pm}\) such that \(Qv^+\leq v^+\) and \(Qv^-\geq v^-\).
Mathematics Subject Classification ID: 90C40
zbMATH DE Number: 3965844
zbMATH Keywords: undiscounted semi-Markovian decision processes
zbMATH Keywords: maximum gain rate vector
MaRDI profile type: Publication
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full work available at URL: 0022-247x(84)90031-3
OpenAlex ID: W2047353100
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description: scientific article; zbMATH DE number 3965844