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@inproceedings{1649044,
author = {Křetínský, Jan and Perez, Guillermo and Raskin, JeanandFrancois},
address = {Dagstuhl},
booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)},
doi = {http://dx.doi.org/10.4230/LIPIcs.CONCUR.2018.8},
keywords = {Learning; Mean-Payoff; Markov decision process; Omega-Regular Specification},
howpublished = {elektronická verze "online"},
language = {eng},
location = {Dagstuhl},
isbn = {978-3-95977-087-3},
pages = {1-18},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
title = {Learning-Based Mean-Payoff Optimization in an Unknown MDP under Omega-Regular Constraints},
year = {2018}
}
TY - JOUR
ID - 1649044
AU - Křetínský, Jan - Perez, Guillermo - Raskin, Jean-Francois
PY - 2018
TI - Learning-Based Mean-Payoff Optimization in an Unknown MDP under Omega-Regular Constraints
PB - Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
CY - Dagstuhl
SN - 9783959770873
KW - Learning
KW - Mean-Payoff
KW - Markov decision process
KW - Omega-Regular Specification
N2 - 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.
ER -
KŘETÍNSKÝ, Jan, Guillermo PEREZ and Jean-Francois RASKIN. Learning-Based Mean-Payoff Optimization in an Unknown MDP under Omega-Regular Constraints. Online. In \textit{29th International Conference on Concurrency Theory (CONCUR 2018)}. Dagstuhl: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2018, p.~1-18. ISBN~978-3-95977-087-3. Available from: https://dx.doi.org/10.4230/LIPIcs.CONCUR.2018.8.
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