Strong 1-optimal stationary policies in denumerable Markov decision processes
type: Item
instance of: scholarly article
title: Strong 1-optimal stationary policies in denumerable Markov decision processes
zbMATH Open document ID: 0654.90097
DOI: 10.1016/0167-6911(88)90113-2
published in: Systems \& Control Letters
publication date: 1988-01-01T00:00:00Z
review text: Consider a Markov decision process with countable state space S, compact action sets and bounded rewards. Let \(V_{\alpha}(\pi,i)\) denote the expected \(\alpha\)-discounted reward under policy \(\pi\), starting in state i. \(\pi\) * is called a strong 1-optimal policy (SOP) if, for each \(i\in S\), \(\lim_{\alpha \to 1}[V_{\alpha}(\pi\) *,i)- \(\sup_{\pi}V_{\alpha}(\pi,i)]=O\). Under a standard set of assumptions (including the simultaneous Doeblin condition) for the existence of a stationary average optimal policy, the author proves that (i) a stationary SOP exists, (ii) any limit point, as \(\alpha\) \(\to 1\), of stationary \(\alpha\)-discounted optimal policies is a (stationary) SOP.
Mathematics Subject Classification ID: 90C40
zbMATH DE Number: 4068651
zbMATH Keywords: Markov decision process
zbMATH Keywords: countable state space
zbMATH Keywords: compact action sets
zbMATH Keywords: bounded rewards
zbMATH Keywords: \(\alpha\)-discounted reward
zbMATH Keywords: strong 1-optimal policy
zbMATH Keywords: simultaneous Doeblin condition
zbMATH Keywords: stationary average optimal policy
author: Rolando Cavazos-Cadena
author: Jean B. Lasserre
MaRDI profile type: Publication
full work available at URL: 0167-6911(88)90113-2
OpenAlex ID: W2038481005
cites work: Discrete Dynamic Programming
cites work: Necessary and sufficient conditions for a bounded solution to the optimality equation in average reward Markov decision chains
cites work: Average, Sensitive and Blackwell Optimal Policies in Denumerable Markov Decision Chains with Unbounded Rewards
cites work: On optimality criteria for dynamic programs with long finite horizons
cites work: Q4771778
cites work: Q4152116
cites work: Conditions for existence of average and Blackwell optimal stationary policies in denumerable Markov decision processes
cites work: Discrete Dynamic Programming with a Small Interest Rate
cites work: Q5615108
cites work: Q5593890
cites work: On Finding Optimal Policies in Discrete Dynamic Programming with No Discounting
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description: scientific article; zbMATH DE number 4068651