CPED-NCBFs: A Conformal Prediction for Expert Demonstration-based Neural Control Barrier Functions

TL;DR

This paper introduces CPED-NCBFs, a conformal prediction-based method to verify neural control barrier functions learned from expert demonstrations, ensuring safety across the entire state space.

Contribution

The paper proposes a novel split-conformal prediction approach for verifying neural control barrier functions, addressing limitations of existing conservative verification methods.

Findings

Effective verification of learned NCBFs demonstrated on point mass systems.

CPED-NCBFs provides less conservative bounds compared to traditional methods.

Validation on unicycle models confirms robustness of the approach.

Abstract

Among the promising approaches to enforce safety in control systems, learning Control Barrier Functions (CBFs) from expert demonstrations has emerged as an effective strategy. However, a critical challenge remains: verifying that the learned CBFs truly enforce safety across the entire state space. This is especially difficult when CBF is represented using neural networks (NCBFs). Several existing verification techniques attempt to address this problem including SMT-based solvers, mixed-integer programming (MIP), and interval or bound-propagation methods but these approaches often introduce loose, conservative bounds. To overcome these limitations, in this work we use CPED-NCBFs a split-conformal prediction based verification strategy to verify the learned NCBF from the expert demonstrations. We further validate our method on point mass systems and unicycle models to demonstrate the effectiveness of the proposed theory.