Stochastic Shortest Paths and Weight-Bounded Properties in Markov Decision Processes

Abstract : The paper deals with finite-state Markov decision processes (MDPs) with integer weights assigned to each state-action pair. New algorithms are presented to classify end components according to their limiting behavior with respect to the accumulated weights. These algorithms are used to provide solutions for two types of fundamental problems for integer-weighted MDPs. First, a polynomial-time algorithm for the classical stochastic shortest path problem is presented, generalizing known results for special classes of weighted MDPs. Second, qualitative probability constraints for weight-bounded (repeated) reachability conditions are addressed. Among others, it is shown that the problem to decide whether a disjunction of weight-bounded reachability conditions holds almost surely under some scheduler belongs to NP ∩ coNP, is solvable in pseudo-polynomial time and is at least as hard as solving two-player mean-payoff games, while the corresponding problem for universal quantification over schedulers is solvable in polynomial time.
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Contributor : Ocan Sankur <>
Submitted on : Friday, September 28, 2018 - 10:23:02 AM
Last modification on : Friday, September 13, 2019 - 9:48:42 AM

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Christel Baier, Nathalie Bertrand, Clemens Dubslaff, Daniel Gburek, Ocan Sankur. Stochastic Shortest Paths and Weight-Bounded Properties in Markov Decision Processes. LICS '18 - 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, Jul 2018, Oxford, United Kingdom. pp.86-94, ⟨10.1145/3209108.3209184⟩. ⟨hal-01883409⟩



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