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DOI: 10.4230/LIPIcs.CONCUR.2020.39
URN: urn:nbn:de:0030-drops-128513
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12851/
Kiefer, Stefan ; Mayr, Richard ; Shirmohammadi, Mahsa ; Totzke, Patrick
Strategy Complexity of Parity Objectives in Countable MDPs
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Abstract
We study countably infinite MDPs with parity objectives. Unlike in finite MDPs, optimal strategies need not exist, and may require infinite memory if they do. We provide a complete picture of the exact strategy complexity of ε-optimal strategies (and optimal strategies, where they exist) for all subclasses of parity objectives in the Mostowski hierarchy. Either MD-strategies, Markov strategies, or 1-bit Markov strategies are necessary and sufficient, depending on the number of colors, the branching degree of the MDP, and whether one considers ε-optimal or optimal strategies. In particular, 1-bit Markov strategies are necessary and sufficient for ε-optimal (resp. optimal) strategies for general parity objectives.
BibTeX - Entry
@InProceedings{kiefer_et_al:LIPIcs:2020:12851,
author = {Stefan Kiefer and Richard Mayr and Mahsa Shirmohammadi and Patrick Totzke},
title = {{Strategy Complexity of Parity Objectives in Countable MDPs}},
booktitle = {31st International Conference on Concurrency Theory (CONCUR 2020)},
pages = {39:1--39:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-160-3},
ISSN = {1868-8969},
year = {2020},
volume = {171},
editor = {Igor Konnov and Laura Kov{\'a}cs},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12851},
URN = {urn:nbn:de:0030-drops-128513},
doi = {10.4230/LIPIcs.CONCUR.2020.39},
annote = {Keywords: Markov decision processes, Parity objectives, Levy’s zero-one law}
}
| Keywords: | Markov decision processes, Parity objectives, Levy’s zero-one law | |
| Seminar: | 31st International Conference on Concurrency Theory (CONCUR 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 26.08.2020 |
