The discounted method and equivalence of average criteria for risk-sensitive Markov decision processes on Borel spaces
type: Item
instance of: scholarly article
title: The discounted method and equivalence of average criteria for risk-sensitive Markov decision processes on Borel spaces
zbMATH Open document ID: 1196.60127
author: Rolando Cavazos-Cadena
author: Francisco Sergio Salem-Silva
published in: Applied Mathematics and Optimization
publication date: 2010-04-20T00:00:00Z
review text: The work concerns discrete-time Markov decision processes evolving on a Borel space. The system is driven by a risk-averse decision maker with a constant risk sensitivity coefficient \(\lambda > 0\), and the performance of a control policy is measured by the (superior limit) risk-sensitive average cost criterion associated with a nonnegative cost function. Under mild (semi-) continuity and compactness conditions, the following problems are studied via the discounted approach: (i) establishing the existence of optimal stationary policies, and (ii) determination of conditions under which the equality of the optimal value functions associated with the inferior limit and superior limit average criteria can be ensured. The approach of the paper relies on standard dynamic programming ideas and on a simple analytical derivation of a Tauberian relation.
reviewed by: Wiesław Kotarski
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 90C40
zbMATH DE Number: 5695466
zbMATH Keywords: Hölder's inequality
zbMATH Keywords: contractive operators
zbMATH Keywords: generalized Fatou's lemma
zbMATH Keywords: risk-sensitive discount approach
zbMATH Keywords: weak continuity
MaRDI profile type: Publication
full work available at URL: s00245-009-9080-2
OpenAlex ID: W2004904423
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DOI: 10.1007/S00245-009-9080-2
description: scientific article; zbMATH DE number 5695466