Conformalized Data-Driven Reachability Analysis with PAC Guarantees

TL;DR

This paper introduces CDDR, a novel framework for data-driven reachability analysis that provides PAC guarantees without requiring known noise bounds or system-specific parameters, applicable to linear and nonlinear systems.

Contribution

The paper proposes CDDR, a new approach that offers PAC guarantees for reachability analysis using conformal methods, applicable to diverse system types without prior noise knowledge.

Findings

CDDR achieves valid coverage where deterministic methods fail.

Normalized score function reduces reachable set volume while maintaining guarantees.

Experiments demonstrate effectiveness on systems with Gaussian, heavy-tailed, and non-Lipschitz dynamics.

Abstract

Data-driven reachability analysis computes over-approximations of reachable sets directly from noisy data. Existing deterministic methods require either known noise bounds or system-specific structural parameters such as Lipschitz constants. We propose Conformalized Data-Driven Reachability (CDDR), a framework that provides Probably Approximately Correct (PAC) coverage guarantees through the Learn Then Test (LTT) calibration procedure, requiring only that calibration and test trajectories be independently and identically distributed. CDDR is developed for three settings: linear time-invariant (LTI) systems with unknown process noise distributions, LTI systems with bounded measurement noise, and general nonlinear systems including non-Lipschitz dynamics. Experiments on a 5-dimensional LTI system under Gaussian and heavy-tailed Student-t noise and on a 2-dimensional non-Lipschitz system with fractional damping demonstrate that CDDR achieves valid coverage where deterministic methods do not provide formal guarantees. Under anisotropic noise, a normalized score function reduces the reachable set volume while preserving the PAC guarantee.