Transfer Learning for Barrier Certificates

Alireza Nadali, Ashutosh Trivedi, Majid Zamani

Abstract: A principled approach to safety verification of dynamical systems demands formal guarantees. Barrier certificates are an effective tool for searching safety proofs in the form of inductively verifiable invariants. However, finding barrier certificates is an expensive and time-consuming process that demands human expertise in selecting various templates, hyperparameters, and decision procedures. Is it possible to transfer the knowledge gained in finding a barrier certificate and control algorithm from a given environment (source environment) to a different but related environment (target environment)? This paper presents a transfer learning approach to adapt the barrier certificates (of any template) in the form of neural networks from the source to the target environment. We derive a validity condition to formally guarantee the correctness of network by leveraging its Lipschitz continuity. To demonstrate the effectiveness of our approach, we apply it to two case studies, namely the inverted pendulum, DC motor and Room temperature control. Our results show that transfer learning can successfully adapt barrier certificates from the source to the target environment, reducing the need for human expertise and speeding up the verification process.