--- _id: '3346' 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>;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>;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. article_number: '5970225' author: - first_name: Tomáš full_name: Brázdil, Tomáš last_name: Brázdil - first_name: Václav full_name: Brožek, Václav last_name: Brožek - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Vojtěch full_name: Forejt, Vojtěch last_name: Forejt - first_name: Antonín full_name: Kučera, Antonín last_name: Kučera citation: 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:10.1109/LICS.2011.10' apa: 'Brázdil, T., Brožek, V., Chatterjee, K., Forejt, V., & 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. https://doi.org/10.1109/LICS.2011.10' 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. https://doi.org/10.1109/LICS.2011.10. 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.' 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.' mla: Brázdil, Tomáš, et al. Two Views on Multiple Mean Payoff Objectives in Markov Decision Processes. 5970225, IEEE, 2011, doi:10.1109/LICS.2011.10. short: T. Brázdil, V. Brožek, K. Chatterjee, V. Forejt, A. Kučera, in:, IEEE, 2011. conference: end_date: 2011-06-24 location: Toronto, Canada name: 'LICS: Logic in Computer Science' start_date: 2011-06-21 date_created: 2018-12-11T12:02:48Z date_published: 2011-06-21T00:00:00Z date_updated: 2021-01-12T07:42:49Z day: '21' department: - _id: KrCh doi: 10.1109/LICS.2011.10 ec_funded: 1 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1104.3489 month: '06' oa: 1 oa_version: Submitted Version project: - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 2587B514-B435-11E9-9278-68D0E5697425 name: Microsoft Research Faculty Fellowship publication_status: published publisher: IEEE publist_id: '3275' quality_controlled: '1' scopus_import: 1 status: public title: Two views on multiple mean payoff objectives in Markov Decision Processes type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2011' ...