Estimating Rewards & Rare Events in Nondeterministic Systems

Abstract

Exhaustive verification can quantify critical behaviour arising from concurrency in nondeterministic models. Rare events typically entail no additional challenge, but complex systems are generally intractable. Recent work on Markov decision processes allows the extremal probabilities of a property to be estimated using Monte Carlo techniques, offering the potential to handle much larger models. Here we present algorithms to estimate extremal rewards and consider the challenges posed by rarity. We find that rewards require a different interpretation of confidence and that reachability rewards require the introduction of an auxiliary hypothesis test. We show how importance sampling can significantly improve estimation when probabilities are low, but find it is not a panacea for rare schedulers.