Runtime Monitoring for Markov Decision Processes

TL;DR

This paper addresses runtime monitoring of partially observable systems with probabilistic and nondeterministic behaviors, proposing scalable algorithms for risk estimation and demonstrating their effectiveness on benchmarks.

Contribution

It introduces a tractable model checking algorithm for risk estimation in partially observable Markov decision processes, overcoming scalability issues of previous methods.

Findings

Convex hull algorithms improve runtime but cause exponential memory growth.

The proposed model checking approach is scalable and effective.

Prototypical implementations demonstrate practical applicability.

Abstract

We investigate the problem of monitoring partially observable systems with nondeterministic and probabilistic dynamics. In such systems, every state may be associated with a risk, e.g., the probability of an imminent crash. During runtime, we obtain partial information about the system state in form of observations. The monitor uses this information to estimate the risk of the (unobservable) current system state. Our results are threefold. First, we show that extensions of state estimation approaches do not scale due the combination of nondeterminism and probabilities. While convex hull algorithms improve the practical runtime, they do not prevent an exponential memory blowup. Second, we present a tractable algorithm based on model checking conditional reachability probabilities. Third, we provide prototypical implementations and manifest the applicability of our algorithms to a range of benchmarks. The results highlight the possibilities and boundaries of our novel algorithms.