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@inproceedings{1174049,
author = {Chatterjee, Krishnendu and Forejt, Vojtěch and Wojtczak, Dominik},
address = {Berlin, Heidelberg},
booktitle = {Logic for Programming, Artificial Intelligence, and Reasoning},
doi = {http://dx.doi.org/10.1007/978-3-642-45221-5_17},
editor = {Kenneth L. McMillan and Aart Middeldorp and Andrei Voronkov},
keywords = {multi-objective verification; markov decision processes; graphs},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Berlin, Heidelberg},
isbn = {978-3-642-45220-8},
pages = {228-242},
publisher = {Springer},
title = {Multi-objective Discounted Reward Verification in Graphs and MDPs},
year = {2013}
}
TY - JOUR
ID - 1174049
AU - Chatterjee, Krishnendu - Forejt, Vojtěch - Wojtczak, Dominik
PY - 2013
TI - Multi-objective Discounted Reward Verification in Graphs and MDPs
PB - Springer
CY - Berlin, Heidelberg
SN - 9783642452208
KW - multi-objective verification
KW - markov decision processes
KW - graphs
N2 - We study the problem of achieving a given value in Markov decision processes (MDPs) with several independent discounted reward objectives. We consider a generalised version of discounted reward objectives, in which the amount of discounting depends on the states visited and on the objective. This definition extends the usual definition of discounted reward, and allows to capture the systems in which the value of different commodities diminish at different and variable rates. We establish results for two prominent subclasses of the problem, namely state-discount models where the discount factors are only dependent on the state of the MDP (and independent of the objective), and reward-discount models where they are only dependent on the objective (but not on the state of the MDP). For the state-discount models we use a straightforward reduction to expected total reward and show that the problem whether a value is achievable can be solved in polynomial time. For the reward-discount model we show that memory and randomisation of the strategies are required, but nevertheless that the problem is decidable and it is sufficient to consider strategies which after a certain number of steps behave in a memoryless way. For the general case, we show that when restricted to graphs (i.e. MDPs with no randomisation), pure strategies and discount factors of the form 1/n where n is an integer, the problem is in PSPACE and finite memory suffices for achieving a given value. We also show that when the discount factors are not of the form 1/n, the memory required by a strategy can be infinite.
ER -
CHATTERJEE, Krishnendu, Vojtěch FOREJT and Dominik WOJTCZAK. Multi-objective Discounted Reward Verification in Graphs and MDPs. In Kenneth L. McMillan and Aart Middeldorp and Andrei Voronkov. \textit{Logic for Programming, Artificial Intelligence, and Reasoning}. Berlin, Heidelberg: Springer, 2013, p.~228-242. ISBN~978-3-642-45220-8. Available from: https://dx.doi.org/10.1007/978-3-642-45221-5\_{}17.
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