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Strong Uniform Value in Gambling Houses and Partially Observable Markov Decision Processes

Venel, Xavier; Ziliotto, Bruno (2016), Strong Uniform Value in Gambling Houses and Partially Observable Markov Decision Processes, SIAM Journal on Control and Optimization, 54, 4, p. 1983-2008. 10.1137/15M1043340

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Type
Article accepté pour publication ou publié
Date
2016
Nom de la revue
SIAM Journal on Control and Optimization
Volume
54
Numéro
4
Éditeur
SIAM - Society for Industrial and Applied Mathematics
Pages
1983-2008
Identifiant publication
Métadonnées
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Auteur(s)
Venel, Xavier cc
Centre d'économie de la Sorbonne [CES]
Ziliotto, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Résumé (EN)
In several standard models of dynamic programming (gambling houses, MDPs, POMDPs), we prove the existence of a robust notion of value for the infinitely repeated problem, namely the strong uniform value. This solves two open problems. First, this shows that for any > 0, the decision-maker has a pure strategy σ which is-optimal in any n-stage problem, provided that n is big enough (this result was only known for behavior strategies, that is, strategies which use randomization). Second, for any > 0, the decision-maker can guarantee the limit of the n-stage value minus in the infinite problem where the payoff is the expectation of the inferior limit of the time average payoff.
Mots-clés
dynamic programming; Markov decision processes; partial observation; uniform value; long-run average payoff