Compositional Value Iteration with Pareto Caching

TL;DR

This paper introduces compositional value iteration with Pareto caching for efficient and sound model checking of compositional MDPs, leveraging component reuse and novel stopping criteria.

Contribution

It presents a new compositional VI framework with Pareto caching for reusing verification results and two sound stopping criteria, enhancing efficiency and correctness.

Findings

Pareto caching enables reuse of verification results.

Experimental results show improved efficiency and potential for future work.

Two stopping criteria ensure soundness in compositional VI.

Abstract

The de-facto standard approach in MDP verification is based on value iteration (VI). We propose compositional VI, a framework for model checking compositional MDPs, that addresses efficiency while maintaining soundness. Concretely, compositional MDPs naturally arise from the combination of individual components, and their structure can be expressed using, e.g., string diagrams. Towards efficiency, we observe that compositional VI repeatedly verifies individual components. We propose a technique called Pareto caching that allows to reuse verification results, even for previously unseen queries. Towards soundness, we present two stopping criteria: one generalizes the optimistic value iteration paradigm and the other uses Pareto caches in conjunction with recent baseline algorithms. Our experimental evaluations shows the promise of the novel algorithm and its variations, and identifies challenges for future work.