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Title
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Learning-based mean-payoff optimization in an unknown MDP under omega-regular constraints
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Author
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Abstract
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| We formalize the problem of maximizing the mean-payoff value with high probability while satisfying a parity objective in a Markov decision process (MDP) with unknown probabilistic transition function and unknown reward function. Assuming the support of the unknown transition function and a lower bound on the minimal transition probability are known in advance, we show that in MDPs consisting of a single end component, two combinations of guarantees on the parity and mean-payoff objectives can be achieved depending on how much memory one is willing to use. (i) For all epsilon and gamma we can construct an online-learning finite-memory strategy that almost-surely satisfies the parity objective and which achieves an epsilon-optimal mean payoff with probability at least 1 - gamma. (ii) Alternatively, for all epsilon and gamma there exists an online-learning infinite-memory strategy that satisfies the parity objective surely and which achieves an epsilon-optimal mean payoff with probability at least 1 - gamma. We extend the above results to MDPs consisting of more than one end component in a natural way. Finally, we show that the aforementioned guarantees are tight, i.e. there are MDPs for which stronger combinations of the guarantees cannot be ensured. |
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Language
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English
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Source (journal)
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LIPIcs : Leibniz International Proceedings in Informatics. - Place of publication unknown
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Source (book)
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29th International Conference on Concurrency Theory (CONCUR 2018) / Schewe, Sven [edit.]; et al.
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Publication
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Germany
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Schloss Dagstuhl, Leibniz-Zentrum fuer Informatik
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2018
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ISSN
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1868-8969
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ISBN
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978-3-95977-087-3
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DOI
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10.4230/LIPICS.CONCUR.2018.8
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Volume/pages
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118
(2018)
, 18 p.
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Article Reference
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8
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Medium
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E-only publicatie
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Full text (Publisher's DOI)
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Full text (open access)
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