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Growth Rates and Average Optimality in Risk-Sensitive Markov Decision Chains
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SYSNO ASEP 0309471 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Growth Rates and Average Optimality in Risk-Sensitive Markov Decision Chains Title Míry růstu a optimality v průměru v rizikových markovských rozhodovacích řetězcích Author(s) Sladký, Karel (UTIA-B) RID Source Title Kybernetika. - : Ústav teorie informace a automatizace AV ČR, v. v. i. - ISSN 0023-5954
Roč. 44, č. 2 (2008), s. 205-226Number of pages 22 s. Language eng - English Country CZ - Czech Republic Keywords risk-sensitive Markov decision chains ; average optimal policies ; optimal growth rates Subject RIV BC - Control Systems Theory R&D Projects GA402/08/0107 GA ČR - Czech Science Foundation (CSF) GA402/07/1113 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10750506 - UTIA-B (2005-2011) UT WOS 000257062200006 Annotation In this note we focus attention on characterization of policies maximizing growth rate of expected utility, along with average of the associated certainty equivalent, in risk-sensitive Markov decision chains with finite state and action spaces. In contrast to existing literature, the problem is handled by methods of stochastic dynamic programming on condition that the transition probabilities are replaced by general nonnegative matrices. Using the block-triangular decomposition of a collection of nonnegative matrices we establish necessary and sufficient condition guaranteeing independence of optimal values on starting state along with partition of the state space into subsets with constant optimal values. Finally for models with growth rate independent of the starting state we show how the method work if we minimize growth rate or average of the certainty equivalent. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2009
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