Verifiable Safety Q-Filters via Hamilton-Jacobi Reachability and Multiplicative Q-Networks
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915350508994560 |
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| author | Li, Jiaxing Hu, Hanjiang Yang, Yujie Liu, Changliu |
| author_facet | Li, Jiaxing Hu, Hanjiang Yang, Yujie Liu, Changliu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15693 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Verifiable Safety Q-Filters via Hamilton-Jacobi Reachability and Multiplicative Q-Networks Li, Jiaxing Hu, Hanjiang Yang, Yujie Liu, Changliu Machine Learning 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. |
| title | Verifiable Safety Q-Filters via Hamilton-Jacobi Reachability and Multiplicative Q-Networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.15693 |