Conformalized Data-Driven Reachability Analysis with PAC Guarantees
This work addresses the challenge of ensuring formal safety guarantees in control systems with uncertain noise, offering a more flexible and robust approach for applications like robotics and autonomous vehicles, though it builds incrementally on existing conformal prediction methods.
The paper tackled the problem of data-driven reachability analysis for systems with noisy data by proposing Conformalized Data-Driven Reachability (CDDR), which provides Probably Approximately Correct (PAC) coverage guarantees without requiring known noise bounds or system-specific parameters, achieving valid coverage where deterministic methods fail in experiments on linear and nonlinear systems.
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 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.