Brázdil, Tomáš ; Brožek, Václav ; Chatterjee, KrishnenduIST Austria ; Forejt, Vojtěch ; Kučera, Antonín
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.
LICS: Logic in Computer Science
2011-06-21 – 2011-06-24
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
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
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.
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.
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
Brázdil, Tomáš, et al. Two Views on Multiple Mean Payoff Objectives in Markov Decision Processes. 5970225, IEEE, 2011, doi:10.1109/LICS.2011.10.
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