Verification-Aided Learning of Neural Network Barrier Functions with
  Termination Guarantees
Shaoru Chen Lekan Molu Mahyar Fazlyab
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.