Stein Variational Uncertainty-Adaptive Model Predictive Control

Abstract

We propose a Stein variational distributionally robust controller for nonlinear dynamical systems with latent parametric uncertainty. The method is an alternative to conservative worst-case ambiguity-set optimization with a deterministic particle-based approximation of a task-dependent uncertainty distribution, enabling the controller to concentrate on parameter sensitivities that most strongly affect closed-loop performance. Our method yields a controller that is robust to latent parameter uncertainty by coupling optimal control with Stein variational inference, and avoiding restrictive parametric assumptions on the uncertainty model while preserving computational parallelism. In contrast to classical DRO, which can sacrifice nominal performance through worst-case design, we find our approach achieves robustness by shaping the control law around relevant uncertainty that are most critical to the task objective. The proposed framework therefore reconciles robust control and variational inference in a single decision-theoretic formulation for broad classes of control systems with parameter uncertainty. We demonstrate our approach on representative control problems that empirically illustrate improved performance-robustness tradeoffs over nominal, ensemble, and classical distributionally robust baselines.

Figures (3)

• Figure 3: Autonomous Racing under Vehicle Inertial Uncertainty. Here, we apply our Stein variational uncertainty-adaptive framework to autonomous racing, where the objective is to minimize lap time under significant uncertainty in the vehicle’s mass distribution (mass and inertia). We compare our approach to current state-of-art control baselines: Ensemble Model Predictive Control (EMPPI) Abraham_2020, Classical Distributionally Robust Control (DRO) kuhn2025distributionallyrobustoptimization, and conventional Model Predictive Control that directly solves the task without the consideration of uncertainty. Our approach optimizes for controls that quickly adapts to task-sensitive uncertainties faster than nominal baselines, enabling fast adaptation and convergence to the racing objective.
• Figure 4: Example Experimental Outcomes from Our Method. We demonstrate the efficacy of our approach on a two-dimensional rocket landing and cartpole swingup control tasks.
• Figure 5: Autonomous Racing Lap Time Completions. Here we report track completion over time for the autonomous racing task under parametric uncertainty in mass and inertia. Our method achieves faster and more consistent progress by reasoning over task-sensitive regions of the parameter posterior, prioritizing parameter realizations that most affect control performance.

Theorems & Definitions (8)

• Remark 1
• Proposition 1: Existence of optimal state-control trajectory
• proof
• Lemma 1: Continuity of the Stein potential
• proof
• Theorem 1
• Theorem 2
• proof