{"abstract":[{"lang":"eng","text":"We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions. We consider two different objectives, namely, expectation and satisfaction objectives. Given an MDP with κ limit-average functions, in the expectation objective the goal is to maximize the expected limit-average value, and in the satisfaction objective the goal is to maximize the probability of runs such that the limit-average value stays above a given vector. We show that under the expectation objective, in contrast to the case of one limit-average function, both randomization and memory are necessary for strategies even for ε-approximation, and that finite-memory randomized strategies are sufficient for achieving Pareto optimal values. Under the satisfaction objective, in contrast to the case of one limit-average function, infinite memory is necessary for strategies achieving a specific value (i.e. randomized finite-memory strategies are not sufficient), whereas memoryless randomized strategies are sufficient for ε-approximation, for all ε &gt; 0. We further prove that the decision problems for both expectation and satisfaction objectives can be solved in polynomial time and the trade-off curve (Pareto curve) can be ε-approximated in time polynomial in the size of the MDP and 1/ε, and exponential in the number of limit-average functions, for all ε &gt; 0. Our analysis also reveals flaws in previous work for MDPs with multiple mean-payoff functions under the expectation objective, corrects the flaws, and allows us to obtain improved results."}],"oa_version":"Published Version","publication":"Logical Methods in Computer Science","citation":{"ama":"Brázdil T, Brožek V, Chatterjee K, Forejt V, Kučera A. Markov decision processes with multiple long-run average objectives. <i>Logical Methods in Computer Science</i>. 2014;10(1). doi:<a href=\"https://doi.org/10.2168/LMCS-10(1:13)2014\">10.2168/LMCS-10(1:13)2014</a>","ista":"Brázdil T, Brožek V, Chatterjee K, Forejt V, Kučera A. 2014. Markov decision processes with multiple long-run average objectives. Logical Methods in Computer Science. 10(1).","short":"T. Brázdil, V. Brožek, K. Chatterjee, V. Forejt, A. Kučera, Logical Methods in Computer Science 10 (2014).","chicago":"Brázdil, Tomáš, Václav Brožek, Krishnendu Chatterjee, Vojtěch Forejt, and Antonín Kučera. “Markov Decision Processes with Multiple Long-Run Average Objectives.” <i>Logical Methods in Computer Science</i>. International Federation of Computational Logic, 2014. <a href=\"https://doi.org/10.2168/LMCS-10(1:13)2014\">https://doi.org/10.2168/LMCS-10(1:13)2014</a>.","apa":"Brázdil, T., Brožek, V., Chatterjee, K., Forejt, V., &#38; Kučera, A. (2014). Markov decision processes with multiple long-run average objectives. <i>Logical Methods in Computer Science</i>. International Federation of Computational Logic. <a href=\"https://doi.org/10.2168/LMCS-10(1:13)2014\">https://doi.org/10.2168/LMCS-10(1:13)2014</a>","ieee":"T. Brázdil, V. Brožek, K. Chatterjee, V. Forejt, and A. Kučera, “Markov decision processes with multiple long-run average objectives,” <i>Logical Methods in Computer Science</i>, vol. 10, no. 1. International Federation of Computational Logic, 2014.","mla":"Brázdil, Tomáš, et al. “Markov Decision Processes with Multiple Long-Run Average Objectives.” <i>Logical Methods in Computer Science</i>, vol. 10, no. 1, International Federation of Computational Logic, 2014, doi:<a href=\"https://doi.org/10.2168/LMCS-10(1:13)2014\">10.2168/LMCS-10(1:13)2014</a>."},"publication_identifier":{"issn":["18605974"]},"ec_funded":1,"month":"02","pubrep_id":"428","department":[{"_id":"KrCh"}],"project":[{"name":"Modern Graph Algorithmic Techniques in Formal Verification","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23","call_identifier":"FWF"},{"grant_number":"S11407","call_identifier":"FWF","name":"Game Theory","_id":"25863FF4-B435-11E9-9278-68D0E5697425"},{"name":"Quantitative Graph Games: Theory and Applications","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307","call_identifier":"FP7"},{"name":"Microsoft Research Faculty Fellowship","_id":"2587B514-B435-11E9-9278-68D0E5697425"}],"issue":"1","language":[{"iso":"eng"}],"author":[{"full_name":"Brázdil, Tomáš","last_name":"Brázdil","first_name":"Tomáš"},{"full_name":"Brožek, Václav","last_name":"Brožek","first_name":"Václav"},{"full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Vojtěch","last_name":"Forejt","full_name":"Forejt, Vojtěch"},{"first_name":"Antonín","last_name":"Kučera","full_name":"Kučera, Antonín"}],"year":"2014","day":"14","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"publisher":"International Federation of Computational Logic","oa":1,"file":[{"date_created":"2018-12-12T10:07:57Z","file_id":"4656","access_level":"open_access","creator":"system","file_size":375388,"checksum":"803edcc2d8c1acfba44a9ec43a5eb9f0","content_type":"application/pdf","file_name":"IST-2016-428-v1+1_1104.3489.pdf","date_updated":"2020-07-14T12:45:34Z","relation":"main_file"}],"file_date_updated":"2020-07-14T12:45:34Z","date_created":"2018-12-11T11:56:29Z","main_file_link":[{"open_access":"1","url":"http://repository.ist.ac.at/id/eprint/428"}],"doi":"10.2168/LMCS-10(1:13)2014","_id":"2234","type":"journal_article","publist_id":"4727","volume":10,"title":"Markov decision processes with multiple long-run average objectives","quality_controlled":"1","date_published":"2014-02-14T00:00:00Z","date_updated":"2021-01-12T06:56:11Z","ddc":["000"],"status":"public","publication_status":"published","scopus_import":1,"intvolume":"        10","has_accepted_license":"1","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87"}