2026-07-22T10:51:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:9546 2024-03-06T10:44:41Z ddc:004 open_access

Learning-Based Mean-Payoff Optimization in an Unknown MDP under Omega-Regular Constraints Kretínský, Jan Pérez, Guillermo A. Raskin, Jean-François Markov decision processes Reinforcement learning Beyond worst case 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jan Kretínský and Guillermo A. Pérez and Jean-François Raskin 2018 Is Part Of LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2018.8 urn:nbn:de:0030-drops-95468 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.8 eng https://creativecommons.org/licenses/by/3.0/legalcode