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

What the math gives to ML

The paper contributes a scalable differentiable safety-filter construction: solve a control-barrier-function quadratic program through operator splitting rather than a dense QP layer, then backpropagate using matrix-free local derivatives. The transferable asset is the decomposition of the layer Jacobian into orthogonal projections associated with the nonnegative-slack set and the affine equality set, which avoids differentiating through a large factorization. This can turn hard-constrained policy outputs into trainable safety-filtered actions for high-dimensional multi-agent systems while preserving the constraint at inference time. The most direct experiment is a nominal neural controller followed by an unrolled CBF-QP splitting layer with a custom vector-Jacobian product, compared against an interior-point or generic differentiable-QP baseline.