
Efficient Strategy Iteration for Mean Payoff in Markov Decision Processes
Markov decision processes (MDPs) are standard models for probabilistic s...
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Partial Policy Iteration for L1Robust Markov Decision Processes
Robust Markov decision processes (MDPs) allow to compute reliable soluti...
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Qualitative MDPs and POMDPs: An OrderOfMagnitude Approximation
We develop a qualitative theory of Markov Decision Processes (MDPs) and ...
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Symbolic Algorithms for Graphs and Markov Decision Processes with Fairness Objectives
Given a model and a specification, the fundamental modelchecking proble...
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Distributionbased objectives for Markov Decision Processes
We consider distributionbased objectives for Markov Decision Processes ...
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An Overview for Markov Decision Processes in Queues and Networks
Markov decision processes (MDPs) in queues and networks have been an int...
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Bounding Fixed Points of SetBased Bellman Operator and Nash Equilibria of Stochastic Games
Motivated by uncertain parameters encountered in Markov decision process...
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Faster Algorithms for Quantitative Analysis of Markov Chains and Markov Decision Processes with Small Treewidth
Discretetime Markov Chains (MCs) and Markov Decision Processes (MDPs) are two standard formalisms in system analysis. Their main associated quantitative objectives are hitting probabilities, discounted sum, and mean payoff. Although there are many techniques for computing these objectives in general MCs/MDPs, they have not been thoroughly studied in terms of parameterized algorithms, particularly when treewidth is used as the parameter. This is in sharp contrast to qualitative objectives for MCs, MDPs and graph games, for which treewidthbased algorithms yield significant complexity improvements. In this work, we show that treewidth can also be used to obtain faster algorithms for the quantitative problems. For an MC with n states and m transitions, we show that each of the classical quantitative objectives can be computed in O((n+m)· t^2) time, given a tree decomposition of the MC that has width t. Our results also imply a bound of O(κ· (n+m)· t^2) for each objective on MDPs, where κ is the number of strategyiteration refinements required for the given input and objective. Finally, we make an experimental evaluation of our new algorithms on lowtreewidth MCs and MDPs obtained from the DaCapo benchmark suite. Our experimental results show that on MCs and MDPs with small treewidth, our algorithms outperform existing wellestablished methods by one or more orders of magnitude.
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