Verification-Aided Learning of Neural Network Barrier Functions with Termination Guarantees
<|reference_start|>Verification-Aided Learning of Neural Network Barrier Functions with Termination Guarantees: Barrier functions are a general framework for establishing a safety guarantee for a system. However, there is no general method for finding these functions. To address this shortcoming, recent approaches use self-supervised learning techniques to learn these functions using training data that are periodically generated by a verification procedure, leading to a verification-aided learning framework. Despite its immense potential in automating barrier function synthesis, the verification-aided learning framework does not have termination guarantees and may suffer from a low success rate of finding a valid barrier function in practice. In this paper, we propose a holistic approach to address these drawbacks. With a convex formulation of the barrier function synthesis, we propose to first learn an empirically well-behaved NN basis function and then apply a fine-tuning algorithm that exploits the convexity and counterexamples from the verification failure to find a valid barrier function with finite-step termination guarantees: if there exist valid barrier functions, the fine-tuning algorithm is guaranteed to find one in a finite number of iterations. We demonstrate that our fine-tuning method can significantly boost the performance of the verification-aided learning framework on examples of different scales and using various neural network verifiers.<|reference_end|>
@article{chen2024verification-aided,
    title={Verification-Aided Learning of Neural Network Barrier Functions with
  Termination Guarantees},
    author={Shaoru Chen, Lekan Molu, Mahyar Fazlyab},
    journal={arXiv preprint arXiv:2403.07308},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.07308},
    primaryClass={cs.LG cs.AI cs.SY eess.SY}
}