SHIELD: Scalable Optimal Control with Certification using Duality and Convexity

2026-05-09

AI Summary

This work addresses the high computational complexity of high-dimensional ℓ₁-regularized convex optimization in stochastic model predictive control (SMPC), which hinders real-time deployment. To overcome this challenge, the authors propose a hierarchical solution algorithm that leverages strong convexity and Lagrangian duality to construct provably safe dual certificates for eliminating redundant constraints and identifying zero-valued variables. Notably, they introduce, for the first time, a Transformer-based neural network to accelerate dual certificate inference. The resulting framework significantly reduces the problem dimensionality while preserving closed-loop feasibility and safety guarantees. Extensive evaluations in multimodal, complex traffic scenarios demonstrate order-of-magnitude computational speedups, thereby validating the practicality of lightweight MPC implementations.

Abstract

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.

Problem

• optimal control
• convex optimization
• constraint reduction
• model predictive control
• certifiable safety

Innovation

• Optimal Control
• Lagrangian Duality
• Convex Optimization
• Constraint Reduction
• Transformer-based Inference