Certificating Safety of Imitation Learning for Autonomous Driving With Learnable Weighted Control Barrier Functions

Imitation learning is increasingly utilized to improve driving performance using real-world data, yet ensuring the safety of its outputs remains a fundamental challenge. While differentiable optimization-based methods are widely employed to enhance safety of imitation planner, their joint training often leads to overly conservative behaviors and limited learning capacity. This letter proposes a novel approach to address these limitations through learnable weighted Control Barrier Functions (wCBFs). These wCBFs extend predefined collision constraints into a weight composition of basis functions, thereby constructing a more expressive constraint space. We design practical basis functions for collisin avoidance to balance interpretability and flexibility in constrained imitation learning, and deal with potential conflicts among CBF components through auxiliary task, stabilizing weight training. The proposed learnable wCBFs are integrated into a differentiable QP framework with one compression mechanism that reduces the number of obstacle avoidance constraints while ensuring safety. This mechanism not only accelerates training but also maintains feasibility. Finally we test our joint training framework for planning models and safety modules on the nuPlan benchmark. Our approach demonstrates less over-constrained in safety-critical scenarios compared to non-learnable CBF methods, while having computational efficiency compared to MPC and filtering-based methods.