{"author":[{"full_name":"Grover, Kush","last_name":"Grover","first_name":"Kush"},{"first_name":"Jan","orcid":"0000-0002-8122-2881","id":"44CEF464-F248-11E8-B48F-1D18A9856A87","last_name":"Kretinsky","full_name":"Kretinsky, Jan"},{"last_name":"Meggendorfer","full_name":"Meggendorfer, Tobias","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","orcid":"0000-0002-1712-2165","first_name":"Tobias"},{"first_name":"Maimilian","last_name":"Weininger","full_name":"Weininger, Maimilian"}],"ddc":["000"],"title":"Anytime guarantees for reachability in uncountable Markov decision processes","has_accepted_license":"1","_id":"12775","oa":1,"date_published":"2022-09-15T00:00:00Z","file":[{"relation":"main_file","date_updated":"2023-09-26T10:43:15Z","access_level":"open_access","success":1,"checksum":"e282e43d3ae0ba6e067b72f4583e13c0","creator":"dernst","date_created":"2023-09-26T10:43:15Z","content_type":"application/pdf","file_id":"14372","file_name":"2022_LIPIcS_Grover.pdf","file_size":960036}],"date_updated":"2023-09-26T10:43:30Z","quality_controlled":"1","language":[{"iso":"eng"}],"month":"09","intvolume":"       243","external_id":{"arxiv":["2008.04824"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","alternative_title":["LIPIcs"],"conference":{"name":"CONCUR: Conference on Concurrency Theory","start_date":"2022-09-13","location":"Warsaw, Poland","end_date":"2022-09-16"},"acknowledgement":"Kush Grover: The author has been supported by the DFG research training group GRK\r\n2428 ConVeY.\r\nMaximilian Weininger: The author has been partially supported by DFG projects 383882557\r\nStatistical Unbounded Verification (SUV) and 427755713 Group-By Objectives in Probabilistic\r\nVerification (GOPro)","status":"public","volume":243,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_identifier":{"issn":["1868-8969"]},"oa_version":"Published Version","type":"conference","scopus_import":"1","license":"https://creativecommons.org/licenses/by/4.0/","publication_status":"published","file_date_updated":"2023-09-26T10:43:15Z","article_number":"11","article_processing_charge":"No","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"day":"15","citation":{"short":"K. Grover, J. Kretinsky, T. Meggendorfer, M. Weininger, in:, 33rd International Conference on Concurrency Theory , Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022.","chicago":"Grover, Kush, Jan Kretinsky, Tobias Meggendorfer, and Maimilian Weininger. “Anytime Guarantees for Reachability in Uncountable Markov Decision Processes.” In <i>33rd International Conference on Concurrency Theory </i>, Vol. 243. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. <a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2022.11\">https://doi.org/10.4230/LIPIcs.CONCUR.2022.11</a>.","apa":"Grover, K., Kretinsky, J., Meggendorfer, T., &#38; Weininger, M. (2022). Anytime guarantees for reachability in uncountable Markov decision processes. In <i>33rd International Conference on Concurrency Theory </i> (Vol. 243). Warsaw, Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2022.11\">https://doi.org/10.4230/LIPIcs.CONCUR.2022.11</a>","ama":"Grover K, Kretinsky J, Meggendorfer T, Weininger M. Anytime guarantees for reachability in uncountable Markov decision processes. In: <i>33rd International Conference on Concurrency Theory </i>. Vol 243. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022. doi:<a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2022.11\">10.4230/LIPIcs.CONCUR.2022.11</a>","ieee":"K. Grover, J. Kretinsky, T. Meggendorfer, and M. Weininger, “Anytime guarantees for reachability in uncountable Markov decision processes,” in <i>33rd International Conference on Concurrency Theory </i>, Warsaw, Poland, 2022, vol. 243.","mla":"Grover, Kush, et al. “Anytime Guarantees for Reachability in Uncountable Markov Decision Processes.” <i>33rd International Conference on Concurrency Theory </i>, vol. 243, 11, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, doi:<a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2022.11\">10.4230/LIPIcs.CONCUR.2022.11</a>.","ista":"Grover K, Kretinsky J, Meggendorfer T, Weininger M. 2022. Anytime guarantees for reachability in uncountable Markov decision processes. 33rd International Conference on Concurrency Theory . CONCUR: Conference on Concurrency Theory, LIPIcs, vol. 243, 11."},"date_created":"2023-03-28T08:09:32Z","year":"2022","department":[{"_id":"KrCh"}],"doi":"10.4230/LIPIcs.CONCUR.2022.11","abstract":[{"lang":"eng","text":"We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a sequence of approximations converging to the true value in the limit, our aim is to obtain an algorithm with guarantees on the precision of the approximation.\r\nAs this problem is undecidable in general, assumptions on the MDP are necessary. Our main contribution is to identify sufficient assumptions that are as weak as possible, thus approaching the \"boundary\" of which systems can be correctly and reliably analyzed. To this end, we also argue why each of our assumptions is necessary for algorithms based on processing finitely many observations.\r\nWe present two solution variants. The first one provides converging lower bounds under weaker assumptions than typical ones from previous works concerned with guarantees. The second one then utilizes stronger assumptions to additionally provide converging upper bounds. Altogether, we obtain an anytime algorithm, i.e. yielding a sequence of approximants with known and iteratively improving precision, converging to the true value in the limit. Besides, due to the generality of our assumptions, our algorithms are very general templates, readily allowing for various heuristics from literature in contrast to, e.g., a specific discretization algorithm. Our theoretical contribution thus paves the way for future practical improvements without sacrificing correctness guarantees."}],"publication":"33rd International Conference on Concurrency Theory "}