SHIELD: Scalable Optimal Control with Certification using Duality and Convexity

TL;DR

SHIELD is a hierarchical algorithm that accelerates convex optimization by safely discarding variables and constraints using duality, with neural network guidance, validated in complex traffic scenarios.

Contribution

It introduces a duality-based method with neural network acceleration for scalable, certifiably safe convex optimization in model predictive control.

Findings

Achieves order-of-magnitude speedups in stochastic MPC.

Maintains safety and feasibility despite constraint reduction.

Validated on complex multi-modal traffic scenarios.

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.