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

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Revision_venel_ziliotto5.pdf (423.0Kb)
Date
2016
Dewey
Analyse
Sujet
dynamic programming; Markov decision processes; partial observation; uniform value; long-run average payoff
Journal issue
SIAM Journal on Control and Optimization
Volume
54
Number
4
Publication date
08-2016
Article pages
1983-2008
Publisher
SIAM - Society for Industrial and Applied Mathematics
DOI
http://dx.doi.org/10.1137/15M1043340
URI
https://basepub.dauphine.fr/handle/123456789/20210
Collections
  • CEREMADE : Publications
Metadata
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Author
Venel, Xavier
15080 Centre d'économie de la Sorbonne [CES]
Ziliotto, Bruno
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (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.

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