Unifying two views on multiple mean-payoff objectives in Markov decision processes Conference Paper


Author(s): Chatterjee, Krishnendu; Komárková, Zuzana; Křetínský, Jan
Title: Unifying two views on multiple mean-payoff objectives in Markov decision processes
Affiliation IST Austria
Abstract: We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There exist two different views: (i) ~the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) ~the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector. We consider optimization with respect to both objectives at once, thus unifying the existing semantics. Precisely, the goal is to optimize the expectation while ensuring the satisfaction constraint. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., Ensure certain probabilistic guarantee). Our main results are as follows: First, we present algorithms for the decision problems, which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Second, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
Keywords: Markov Decision Processes; mean payoff; Limit average reward
Conference Title: LICS: Logic in Computer Science
Conference Dates: July 6-10, 2015
Conference Location: Kyoto, Japan
ISBN: 978-147998875-4
Publisher: IEEE  
Date Published: 2015-07-01
Start Page: 244
End Page: 256
DOI: 10.1109/LICS.2015.32
Notes: This research was funded in part by Austrian Science Fund (FWF) Grant No P 23499-N23, FWF NFN Grant No S11407-N23 (RiSE) and Z211-N23 (Wittgenstein Award), European Research Council (ERC) Grant No 279307 (Graph Games), ERC Grant No 267989 (QUAREM), the Czech Science Foundation Grant No P202/12/G061, and People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) REA Grant No 291734. A Technical Report of this paper is available at: https://repository.ist.ac.at/327
Open access: yes (repository)
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