文章基本信息

标题：Learning-Based Mean-Payoff Optimization in an Unknown MDP under Omega-Regular Constraints
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作者：Jan Kret{\'i}nsk{\'y ; Guillermo A. P{\'e}rez ; Jean-Fran{\c{c}}ois Raskin 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2018
卷号：118
页码：1-18
DOI：10.4230/LIPIcs.CONCUR.2018.8
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Markov decision processes; Reinforcement learning; Beyond worst case