Staggered Integral Online Conformal Prediction for Safe Dynamics Adaptation with Multi-Step Coverage Guarantees

arXiv cs.RO / 4/8/2026

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Key Points

The paper argues that standard online conformal prediction cannot reliably quantify uncertainty for adaptive dynamics when state derivatives are not measured, limiting safety guarantees for uncertain adaptive systems.
It introduces Staggered Integral Online Conformal Prediction (SI-OCP), which uses an integral score function to bound the combined effects of disturbances and learning error.
SI-OCP is designed to deliver long-run (long-horizon) coverage guarantees, enabling sustained safety when paired with safety-critical controllers.
The method is demonstrated via numerical simulation on an all-layer deep neural network adaptive quadcopter using robust tube model predictive control, showing applicability to complex DNN-based parameterizations.
The work positions SI-OCP as a way to move beyond overly conservative worst-case uncertainty bounds to improve performance while maintaining provable safety coverage over time.

Abstract

Safety-critical control of uncertain, adaptive systems often relies on conservative, worst-case uncertainty bounds that limit closed-loop performance. Online conformal prediction is a powerful data-driven method for quantifying uncertainty when truth values of predicted outputs are revealed online; however, for systems that adapt the dynamics without measurements of the state derivatives, standard online conformal prediction is insufficient to quantify the model uncertainty. We propose Staggered Integral Online Conformal Prediction (SI-OCP), an algorithm utilizing an integral score function to quantify the lumped effect of disturbance and learning error. This approach provides long-run coverage guarantees, resulting in long-run safety when synthesized with safety-critical controllers, including robust tube model predictive control. Finally, we validate the proposed approach through a numerical simulation of an all-layer deep neural network (DNN) adaptive quadcopter using robust tube MPC, highlighting the applicability of our method to complex learning parameterizations and control strategies.