End-to-End Learning of Safe Optimal Feedback Control in High Dimensions with Control Barrier Function Layers

2026/07/22 by Xingjian Li, Kelvin Kan, Deepanshu Verma +3
#cs.LG #cs.SY #eess.SY #math.OC

paper · pdf

Abstract

We consider the problem of learning high-dimensional semi-global feedback controllers under hard safety constraints enforced by control barrier functions (CBFs). Incorporating CBFs into end-to-end policy training requires embedding a quadratic-program-based safety filter as an optimization layer, but computational and differentiation bottlenecks have largely restricted prior approaches to low-dimensional systems, typically with at most 16 state dimensions. We address this limitation by combining operator splitting with the recently developed Jacobian-Free Backpropagation (JFB) method to enable scalable end-to-end training while preserving hard safety guarantees through the CBF safety filter. We justify this training methodology theoretically using nonsmooth analysis techniques and demonstrate its effectiveness on high-dimensional multi-agent nonlinear control problems with state and control dimensions up to 1200 and 400, respectively.

Citations

• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Optimization Methods for Large-Scale Machine Learning
• Optimization Methods for Large-Scale Machine Learning
• Deep Residual Learning for Image Recognition

Related

• Safe Control Under Input Limits with Neural Control Barrier Functions
• State-action control barrier functions: Imposing safety on learning-based control with low online computational costs
• Learning a Better Control Barrier Function
• On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approach
• Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environments