How Much Do Your Models Disagree? Adaptive MPC Safety From Ensemble Uncertainty

Abstract

Prediction errors of learned dynamics models vary across the state space, so a fixed safety margin is either too conservative where the model is accurate or too aggressive where it is not. We propose Ensemble-Aware Model Predictive Control (EA-MPC), which turns ensemble disagreement into state-dependent safety margins: it propagates a covariance capturing process noise and model disagreement and inflates obstacle constraints with one of three concentration inequalities: Chebyshev, Cantelli (tighter through one-sided geometry, at the same second-moment assumption), and Gaussian (tightest at these risk levels, under a distributional assumption). The covariance-bound schedule stays bounded, and we lift the per-step margins to the trajectory level via a Bonferroni correction (a union bound given per-step margins) and a steady-state correction (a practical approximation, conservative in our runs). On benchmarks with nonlinear dynamics and systematic mismatch, the bounds trace a cost–safety frontier: the distribution-free bound cuts constraint violations by 76% versus certainty-equivalent control, while the tighter margins reduce cost at the expense of more violations, under mild aggregate undercoverage. We compare EA-MPC against a data-driven quantile-tube baseline and validate it on an underactuated quadrotor, matching well-tuned fixed margins without manually tuning a fixed obstacle margin.