eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-08-20
8:1
8:18
10.4230/LIPIcs.CONCUR.2019.8
article
Life Is Random, Time Is Not: Markov Decision Processes with Window Objectives
Brihaye, Thomas
1
Delgrange, Florent
1
2
Oualhadj, Youssouf
3
Randour, Mickael
4
UMONS - Université de Mons, Belgium
RWTH Aachen, Germany
LACL - UPEC, Paris, France
F.R.S.-FNRS & UMONS - Université de Mons, Belgium
The window mechanism was introduced by Chatterjee et al. [Krishnendu Chatterjee et al., 2015] to strengthen classical game objectives with time bounds. It permits to synthesize system controllers that exhibit acceptable behaviors within a configurable time frame, all along their infinite execution, in contrast to the traditional objectives that only require correctness of behaviors in the limit. The window concept has proved its interest in a variety of two-player zero-sum games, thanks to the ability to reason about such time bounds in system specifications, but also the increased tractability that it usually yields. In this work, we extend the window framework to stochastic environments by considering the fundamental threshold probability problem in Markov decision processes for window objectives. That is, given such an objective, we want to synthesize strategies that guarantee satisfying runs with a given probability. We solve this problem for the usual variants of window objectives, where either the time frame is set as a parameter, or we ask if such a time frame exists. We develop a generic approach for window-based objectives and instantiate it for the classical mean-payoff and parity objectives, already considered in games. Our work paves the way to a wide use of the window mechanism in stochastic models.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol140-concur2019/LIPIcs.CONCUR.2019.8/LIPIcs.CONCUR.2019.8.pdf
Markov decision processes
window mean-payoff
window parity