Scalable Tube-Tightened Multi-Agent Safety via Certified Constraint Reduction

What the math gives to ML

The paper offers a constructive mechanism for reducing large collections of linear safety constraints while preserving a certified admissible control set: omitted halfspaces are proved redundant by nonnegative conic combinations of retained halfspaces using Farkas certificates. In planar input spaces, the retained set can be selected from extreme constraint directions using the largest angular gap, with escalation from two to three or more constraints when certification fails. The transferable neural-network design is a certified action-shield or differentiable safety layer for multi-agent reinforcement learning and learned controllers that prunes pairwise collision constraints before solving the final projection or quadratic program, while guaranteeing that the reduced layer accepts no unsafe action accepted by the full tightened layer.