We introduce the problem of formally verifying properties of Markov processes where the parameters are given by the output of machine learning models. For a broad class of machine learning models, including linear models, tree-based models, and neural networks, verifying properties of Markov chains like reachability, hitting time, and total reward can be formulated as a bilinear program. We develop a decomposition and bound propagation scheme for solving the bilinear program and show through computational experiments that our method solves the problem to global optimality up to 100x faster than state-of-the-art solvers. To demonstrate the practical utility of our approach, we apply it to a real-world healthcare case study. Along with the paper, we release markovml, an open-source tool for building Markov processes, integrating pretrained machine learning models, and verifying their properties, available atthis https URL.
View on arXiv@article{maaz2025_2501.15767,
title={ Formal Verification of Markov Processes with Learned Parameters },
author={ Muhammad Maaz and Timothy C. Y. Chan },
journal={arXiv preprint arXiv:2501.15767},
year={ 2025 }
}