Scenario-Based Verification of Uncertain Parametric MDPs
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We consider parametric Markov decision processes (pMDPs) that are augmented with unknown probability distributions over parameter values. The problem is to compute the probability to satisfy a temporal logic specification within any concrete MDP that corresponds to a sample from these distributions. As this problem is infeasible to solve precisely, we resort to sampling techniques that exploit the so-called scenario approach. Based on a finite number of samples of the parameters, the proposed method yields high-confidence bounds on the probability of satisfying the specification. The number of samples required to obtain a high confidence on these bounds is independent of the number of states and the number of random parameters. Experiments on a large set of benchmarks show that several thousand samples suffice to obtain tight and high-confidence lower and upper bounds on the satisfaction probability.
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