Symblicit algorithms for optimal strategy synthesis in monotonic Markov decision processes

Aaron Bohy
(Université de Mons)
Véronique Bruyère
(Université de Mons)
Jean-François Raskin
(Université Libre de Bruxelles)

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 LTL synthesis, we report promising experimental results w.r.t. both the run time and the memory consumption.

In Krishnendu Chatterjee, Rüdiger Ehlers and Susmit Jha: Proceedings 3rd Workshop on Synthesis (SYNT 2014), Vienna, Austria, July 23-24, 2014, Electronic Proceedings in Theoretical Computer Science 157, pp. 51–67.
Published: 18th July 2014.

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