{"date_updated":"2021-01-12T07:42:49Z","publist_id":"3275","type":"conference","language":[{"iso":"eng"}],"_id":"3346","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1104.3489"}],"conference":{"location":"Toronto, Canada","name":"LICS: Logic in Computer Science","end_date":"2011-06-24","start_date":"2011-06-21"},"author":[{"last_name":"Brázdil","first_name":"Tomáš","full_name":"Brázdil, Tomáš"},{"full_name":"Brožek, Václav","first_name":"Václav","last_name":"Brožek"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu"},{"last_name":"Forejt","full_name":"Forejt, Vojtěch","first_name":"Vojtěch"},{"full_name":"Kučera, Antonín","first_name":"Antonín","last_name":"Kučera"}],"doi":"10.1109/LICS.2011.10","quality_controlled":"1","scopus_import":1,"title":"Two views on multiple mean payoff objectives in Markov Decision Processes","publication_status":"published","article_number":"5970225","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 k reward 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 single-objective case, both randomization and memory are necessary for strategies, and that finite-memory randomized strategies are sufficient. Under the satisfaction objective, in contrast to the single-objective case, infinite memory is necessary for strategies, and that randomized memoryless strategies are sufficient for epsilon-approximation, for all epsilon&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 epsilon-approximated in time polynomial in the size of the MDP and 1/epsilon, and exponential in the number of reward functions, for all epsilon&gt;;0. Our results also reveal flaws in previous work for MDPs with multiple mean-payoff functions under the expectation objective, correct the flaws and obtain improved results."}],"oa_version":"Submitted Version","department":[{"_id":"KrCh"}],"citation":{"mla":"Brázdil, Tomáš, et al. <i>Two Views on Multiple Mean Payoff Objectives in Markov Decision Processes</i>. 5970225, IEEE, 2011, doi:<a href=\"https://doi.org/10.1109/LICS.2011.10\">10.1109/LICS.2011.10</a>.","ama":"Brázdil T, Brožek V, Chatterjee K, Forejt V, Kučera A. Two views on multiple mean payoff objectives in Markov Decision Processes. In: IEEE; 2011. doi:<a href=\"https://doi.org/10.1109/LICS.2011.10\">10.1109/LICS.2011.10</a>","short":"T. Brázdil, V. Brožek, K. Chatterjee, V. Forejt, A. Kučera, in:, IEEE, 2011.","ieee":"T. Brázdil, V. Brožek, K. Chatterjee, V. Forejt, and A. Kučera, “Two views on multiple mean payoff objectives in Markov Decision Processes,” presented at the LICS: Logic in Computer Science, Toronto, Canada, 2011.","chicago":"Brázdil, Tomáš, Václav Brožek, Krishnendu Chatterjee, Vojtěch Forejt, and Antonín Kučera. “Two Views on Multiple Mean Payoff Objectives in Markov Decision Processes.” IEEE, 2011. <a href=\"https://doi.org/10.1109/LICS.2011.10\">https://doi.org/10.1109/LICS.2011.10</a>.","ista":"Brázdil T, Brožek V, Chatterjee K, Forejt V, Kučera A. 2011. Two views on multiple mean payoff objectives in Markov Decision Processes. LICS: Logic in Computer Science, 5970225.","apa":"Brázdil, T., Brožek, V., Chatterjee, K., Forejt, V., &#38; Kučera, A. (2011). Two views on multiple mean payoff objectives in Markov Decision Processes. Presented at the LICS: Logic in Computer Science, Toronto, Canada: IEEE. <a href=\"https://doi.org/10.1109/LICS.2011.10\">https://doi.org/10.1109/LICS.2011.10</a>"},"month":"06","date_created":"2018-12-11T12:02:48Z","project":[{"call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23"},{"name":"Rigorous Systems Engineering","call_identifier":"FWF","_id":"25832EC2-B435-11E9-9278-68D0E5697425","grant_number":"S 11407_N23"},{"grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7"},{"name":"Microsoft Research Faculty Fellowship","_id":"2587B514-B435-11E9-9278-68D0E5697425"}],"status":"public","publisher":"IEEE","year":"2011","ec_funded":1,"day":"21","date_published":"2011-06-21T00:00:00Z","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","oa":1}