SHIELD: Scalable Optimal Control with Certification using Duality and Convexity
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| Format: | Preprint |
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2026
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| author | Kim, Hansung Nair, Siddharth H. Borrelli, Francesco |
| author_facet | Kim, Hansung Nair, Siddharth H. Borrelli, Francesco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09171 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SHIELD: Scalable Optimal Control with Certification using Duality and Convexity Kim, Hansung Nair, Siddharth H. Borrelli, Francesco Robotics 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. |
| title | SHIELD: Scalable Optimal Control with Certification using Duality and Convexity |
| topic | Robotics |
| url | https://arxiv.org/abs/2605.09171 |