SHIELD: Scalable Optimal Control with Certification using Duality and Convexity
For real-time control in complex traffic scenarios, SHIELD provides certifiably safe and computationally efficient MPC, enabling practical deployment.
SHIELD reduces decision-variable dimension and constraint set in ℓ1-regularized convex programs using duality and convexity, achieving order-of-magnitude computational speedups in stochastic MPC for traffic scenarios while preserving feasibility and safety.
We present SHIELD, a hierarchical algorithm that reduces both the decision-variable dimension and the constraint set in $\ell_1$-regularized convex programs. From strong convexity and Lagrangian duality, we derive certificates that \emph{safely} discard constraints and decision variables while guaranteeing that all removed constraints remain satisfied and all removed variables are null. To further accelerate the proposed algorithm, we propose a transformer-based deep neural network to guide the dual certificate inference. We validate SHIELD on stochastic model predictive control (SMPC) in complex, multi-modal traffic scenarios, comparing against a full-dimensional SMPC policy. Numerical simulations demonstrate order-of-magnitude computational speedups while preserving feasibility and closed-loop safety, highlighting the practicality of certifiably safe, lightweight MPC in complex driving scenes.