Formal Verification of Markov Processes with Learned Parameters

2025-01-27

AI Summary

This work addresses the formal verification of Markov processes parameterized by machine learning models—including linear regressors, decision trees, and neural networks—to ensure reliability in safety-critical applications such as medical modeling and probabilistic programming. Methodologically, we embed ML parameters into Markov processes and formulate a bilinear programming model; we further propose a novel parameter decomposition technique coupled with interval-bound propagation to enable efficient, globally optimal verification of key properties—including reachability, hitting time, and total reward. Our approach achieves up to 100× speedup over state-of-the-art solvers. We release MarkovML, an open-source tool supporting high-level modeling, seamless ML integration, and end-to-end automated verification. This framework advances formal analysis of AI-augmented stochastic systems, bridging the gap between learning-based components and rigorous probabilistic guarantees.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Security and privacy of machine learning and AI applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

We introduce the problem of formally verifying properties of Markov processes where the parameters are the output of machine learning models. Our formulation is general and solves a wide range of problems, including verifying properties of probabilistic programs that use machine learning, and subgroup analysis in healthcare modeling. We show that 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. We also release $ exttt{markovml}$, an open-source tool for building Markov processes, integrating pretrained machine learning models, and verifying their properties, available at https://github.com/mmaaz-git/markovml.

Problem

• Markov Process
• Machine Learning
• Parameter Validation

Innovation

• Bilinear Programming
• Markov Models Validation
• Optimization in Machine Learning