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Enumeration-Guided Training of Neural Hamilton-Jacobi Safety Certificates

Mihaela-Larisa Clement, Tosca Pierro, Ezio Bartocci, Luca Marzari · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27870 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

汉密尔顿-杰科比(HJ)安全可行性分析为控制系统提供正式的安全保障,但训练准确的神经证书仍然困难,特别是当不安全地区难以特征时。我们提出了一套以验证为导向的培训框架,该框架通过使用安全限制的概率列表来检测前进不变性侵犯,也就是说,在学习证书错误地分类不安全行为的情况下,这产生了一组紧凑的,有针对性的对比示例,该框架比标准对抗攻击方法产生的输入更准确地捕捉失败边界。关键是,使用此表示来精确调整前进不变性侵犯,即学到的HJ值函数产生更大的认证区域,并在所有测试的安全基准之间缩短认证时间。我们进一步引入

Machine translation (Meta M2M100); the English original follows.

Abstract

Hamilton-Jacobi (HJ) reachability analysis offers formal safety guarantees for control systems, but training accurate neural certificates remains difficult, particularly when unsafe regions are hard to characterize. We propose a verification-guided training framework that addresses this by using probabilistic enumeration of safety constraints to detect forward-invariance violations, i.e., states where the learned certificate incorrectly classifies unsafe behavior. This produces a compact, targeted set of counterexamples that more precisely captures the failure boundary than inputs generated by standard adversarial attack methods. Crucially, using this representation to fine-tune a pretrained HJ value function yields larger certified regions and reduces certification time across all tested benchmarks. We further introduce a shielding mechanism based on the refined certificates to enforce safety constraints at deployment time. We evaluate the proposed safety filter in a realistic, physics-based Isaac Sim environment and through real-world autonomous racing experiments, achieving zero safety constraint violations compared to a nominal controller and a backup policy based on Linear Quadratic Regulation (LQR). These results demonstrate the effectiveness of the proposed shielding mechanism in ensuring safe operation under high-speed, safety-critical conditions.

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Topics: Computer science, Certification, Probabilistic logic, Backup, Certificate, System safety

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