Symblicit algorithms for mean-payoff and shortest path in monotonic Markov decision processes

Symblicit algorithms for mean-payoff and shortest path in monotonic Markov decision processes When treating Markov decision processes (MDPs) with large state spaces, using explicit representations quickly becomes unfeasible. Lately, Wimmer et al. have proposed a so-called symblicit algorithm for the synthesis of optimal strategies in MDPs, in the quantitative setting of expected mean-payoff. This algorithm, based on the strategy iteration algorithm of Howard and Veinott, efficiently combines symbolic and explicit data structures, and uses binary decision diagrams as symbolic representation. The aim of this paper is to show that the new data structure of pseudo-antichains (an extension of antichains) provides another interesting alternative, especially for the class of monotonic MDPs. We design efficient pseudo-antichain based symblicit algorithms (with open source implementations) for two quantitative settings: the expected mean-payoff and the stochastic shortest path. For two practical applications coming from automated planning and $$\mathsf {LTL}$$ LTL synthesis, we report promising experimental results w.r.t. both the run time and the memory consumption. We also show that a variant of pseudo-antichains allows to handle the infinite state spaces underlying the qualitative verification of probabilistic lossy channel systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Informatica Springer Journals

Symblicit algorithms for mean-payoff and shortest path in monotonic Markov decision processes

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Computer Science; Logics and Meanings of Programs; Computer Systems Organization and Communication Networks; Software Engineering/Programming and Operating Systems; Data Structures, Cryptology and Information Theory; Theory of Computation; Information Systems and Communication Service
ISSN
0001-5903
eISSN
1432-0525
D.O.I.
10.1007/s00236-016-0255-4
Publisher site
See Article on Publisher Site

Abstract

When treating Markov decision processes (MDPs) with large state spaces, using explicit representations quickly becomes unfeasible. Lately, Wimmer et al. have proposed a so-called symblicit algorithm for the synthesis of optimal strategies in MDPs, in the quantitative setting of expected mean-payoff. This algorithm, based on the strategy iteration algorithm of Howard and Veinott, efficiently combines symbolic and explicit data structures, and uses binary decision diagrams as symbolic representation. The aim of this paper is to show that the new data structure of pseudo-antichains (an extension of antichains) provides another interesting alternative, especially for the class of monotonic MDPs. We design efficient pseudo-antichain based symblicit algorithms (with open source implementations) for two quantitative settings: the expected mean-payoff and the stochastic shortest path. For two practical applications coming from automated planning and $$\mathsf {LTL}$$ LTL synthesis, we report promising experimental results w.r.t. both the run time and the memory consumption. We also show that a variant of pseudo-antichains allows to handle the infinite state spaces underlying the qualitative verification of probabilistic lossy channel systems.

Journal

Acta InformaticaSpringer Journals

Published: Feb 1, 2016

References

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