We present SHIELD, a hierarchical algorithm that reduces both the decision-variable dimension and the constraint set in ℓ1-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.
@article{arxiv.2605.09171,
title = {SHIELD: Scalable Optimal Control with Certification using Duality and Convexity},
author = {Hansung Kim and Siddharth H. Nair and Francesco Borrelli},
journal= {arXiv preprint arXiv:2605.09171},
year = {2026}
}