We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables.
The probability distributions for these random parameters are unknown.
The problem is to compute the probability to satisfy a temporal logic specification within  any MDP that corresponds to a sample from these unknown distributions.
In general, this problem is undecidable, and we resort to techniques from so-called scenario optimization. 
Based on a finite number of samples of the uncertain parameters, each of which induces an MDP, the proposed method estimates the probability of satisfying the specification by solving a finite-dimensional convex optimization problem. 
The number of samples required to obtain a high confidence on this estimate is independent from the number of states and the number of random parameters. 
Experiments on a large set of benchmarks show that a few thousand samples suffice to obtain high-quality confidence bounds with a high probability.

Scenario-Based Verification of Uncertain MDPs

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