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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

Portuguese

A análise de alcançabilidade de Hamilton-Jacobi (HJ) oferece garantias formais de segurança para sistemas de controle, mas o treinamento de certificados neurais precisos permanece difícil, especialmente quando as regiões inseguras são difíceis de caracterizar. Propomos um quadro de treinamento orientado por verificação que aborda isso usando a enumeração probabilística de restrições de segurança para detectar violações de invariância para a frente, ou seja, estados em que o certificado aprendido classifica incorretamente comportamento inseguro. Isso produz um conjunto compacto e direcionado de contra-exemplos que captura com mais precisão o limite de falha do que as entradas geradas por métodos de ataque adversário padrão. Crucialmente, usando esta representação para finalizar uma função de valor HJ pré-treinado resulta em regiões certificadas maiores

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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