Krishnendu Chatterjee ; Zuzana Křetínská ; Jan Křetínský - Unifying Two Views on Multiple Mean-Payoff Objectives in Markov Decision Processes

lmcs:3757 - Logical Methods in Computer Science, July 3, 2017, Volume 13, Issue 2 - https://doi.org/10.23638/LMCS-13(2:15)2017
Unifying Two Views on Multiple Mean-Payoff Objectives in Markov Decision ProcessesArticle

Authors: Krishnendu Chatterjee ; Zuzana Křetínská ; Jan Křetínský

    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.


    Volume: Volume 13, Issue 2
    Published on: July 3, 2017
    Accepted on: July 3, 2017
    Submitted on: July 3, 2017
    Keywords: Computer Science - Logic in Computer Science
    Funding:
      Source : OpenAIRE Graph
    • International IST Postdoctoral Fellowship Programme; Funder: European Commission; Code: 291734
    • Quantitative Graph Games: Theory and Applications; Funder: European Commission; Code: 279307
    • Formal methodes for the design and analysis of complex systems; Funder: Austrian Science Fund (FWF); Code: Z 211
    • Quantitative Reactive Modeling; Funder: European Commission; Code: 267989
    • Modern Graph Algorithmic Techniques in Formal Verification; Funder: Austrian Science Fund (FWF); Code: P 23499

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