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Model-Free Reinforcement Learning for Lexicographic Omega-Regular Objectives

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Formal Methods (FM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 13047))

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Abstract

We study the problem of finding optimal strategies in Markov decision processes with lexicographic \(\omega \)-regular objectives, which are ordered collections of ordinary \(\omega \)-regular objectives. The goal is to compute strategies that maximise the probability of satisfaction of the first \(\omega \)-regular objective; subject to that, the strategy should also maximise the probability of satisfaction of the second \(\omega \)-regular objective; then the third and so forth. For instance, one may want to guarantee critical requirements first, functional ones second and only then focus on the non-functional ones. We show how to harness the classic off-the-shelf model-free reinforcement learning techniques to solve this problem and evaluate their performance on four case studies.

This work was supported by the Engineering and Physical Sciences Research Council through grant EP/P020909/1 and by the National Science Foundation through grant 2009022. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreements No 101032464 (SyGaST), 864075 (CAESAR), and 956123 (FOCETA).

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Notes

  1. 1.

    http://prismmodelchecker.org/casestudies/virus.php.

  2. 2.

    http://prismmodelchecker.org/casestudies/human-uav.php.

  3. 3.

    https://en.wikipedia.org/wiki/Seven_Bridges_of_Konigsberg.

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Author information

Authors and Affiliations

  1. University of Twente, Enschede, The Netherlands

    Ernst Moritz Hahn

  2. University of Colorado Boulder, Boulder, USA

    Mateo Perez, Fabio Somenzi & Ashutosh Trivedi

  3. University of Liverpool, Liverpool, UK

    Sven Schewe & Dominik Wojtczak

Authors
  1. Ernst Moritz Hahn
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  2. Mateo Perez
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  3. Sven Schewe
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  4. Fabio Somenzi
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  5. Ashutosh Trivedi
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  6. Dominik Wojtczak
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Corresponding author

Correspondence to Ashutosh Trivedi .

Editor information

Editors and Affiliations

  1. University of Twente, Enschede, The Netherlands

    Marieke Huisman

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Corina Păsăreanu

  3. Institute of Software, Chinese Academy of Sciences, Beijing, China

    Naijun Zhan

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Hahn, E.M., Perez, M., Schewe, S., Somenzi, F., Trivedi, A., Wojtczak, D. (2021). Model-Free Reinforcement Learning for Lexicographic Omega-Regular Objectives. In: Huisman, M., Păsăreanu, C., Zhan, N. (eds) Formal Methods. FM 2021. Lecture Notes in Computer Science(), vol 13047. Springer, Cham. https://doi.org/10.1007/978-3-030-90870-6_8

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  • DOI: https://doi.org/10.1007/978-3-030-90870-6_8

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