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arXiv · 2506.15693

Verifiable Safety Q-Filters via Hamilton-Jacobi Reachability and Multiplicative Q-Networks

Jiaxing Li·Hanjiang Hu·Yujie Yang·Changliu Liu
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Abstract

Recent learning-based safety filters have outperformed conventional methods, such as hand-crafted Control Barrier Functions (CBFs), by effectively adapting to complex constraints. However, these learning-based approaches lack formal safety guarantees. In this work, we introduce a verifiable model-free safety filter based on Hamilton-Jacobi reachability analysis. Our primary contributions include: 1) extending verifiable self-consistency properties for Q value functions, 2) proposing a multiplicative Q-network structure to mitigate zero-sublevel-set shrinkage issues, and 3) developing a verification pipeline capable of soundly verifying these self-consistency properties. Our proposed approach successfully synthesizes formally verified, model-free safety certificates across four standard safe-control benchmarks.

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Jiaxing Li, Hanjiang Hu, Yujie Yang, Changliu Liu. 2025-05-27. Verifiable Safety Q-Filters via Hamilton-Jacobi Reachability and Multiplicative Q-Networks. https://arxiv.org/abs/2506.15693

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