2020 # Scenario-Based Verification of Uncertain MDPs

**Abstract:** 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. B…

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“…These are used to evaluate e.g., robustness of systems [1], or to synthesise POMDP controllers [43]. Many state-of-the-art approaches [19,26,21] require the evaluation of various instantiated Markov chains, and Rubicon shows it is well-suited to this setting. More generally, support of inference techniques opens the door to a variety of algorithms for additional queries, e.g, computing conditional probabilities [3,8].…”

confidence: 99%

“…These are used to evaluate e.g., robustness of systems [1], or to synthesise POMDP controllers [43]. Many state-of-the-art approaches [19,26,21] require the evaluation of various instantiated Markov chains, and Rubicon shows it is well-suited to this setting. More generally, support of inference techniques opens the door to a variety of algorithms for additional queries, e.g, computing conditional probabilities [3,8].…”

confidence: 99%

“…Contributions. This paper revises an earlier conference paper [20] as follows. Due to new results in [29] that lift some assumptions required for the scenario approach, we can simplify and generalize our approach by a simplified chance-constrained program.…”

confidence: 91%

“…This change in the approach yields completely revised technical sections of the paper. Furthermore, this paper fixes a technical error in [20]. The (new) bounds in Theorem 1 of this paper are less pessimistic.…”

confidence: 94%

“…Further variations of parameter synthesis, e.g., consider statistical guarantees for parameter synthesis, often with some prior on the parameter values [34]- [36]. These approaches cannot provide the absolute guarantees on an answer that the methods in this paper provide.…”

confidence: 98%