Scenario-Based Verification of Uncertain MDPs

Murat Cubuktepe; Nils Jansen; Sebastian Junges; Joost-Pieter Katoen; Ufuk Topcu

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arXiv · 1912.11223

Scenario-Based Verification of Uncertain MDPs

Murat Cubuktepe·Nils Jansen·Sebastian Junges·Joost-Pieter Katoen·Ufuk Topcu

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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. 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.

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BibTeX RIS

Murat Cubuktepe, Nils Jansen, Sebastian Junges, Joost-Pieter Katoen, Ufuk Topcu. 2019-12-24. Scenario-Based Verification of Uncertain MDPs. https://arxiv.org/abs/1912.11223

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