Conformal Reachability for Safe Control in Unknown Environments

TL;DR

This paper introduces a probabilistic verification framework combining conformal prediction and reachability analysis to ensure safe control in unknown dynamical systems, providing strong safety guarantees while maintaining high rewards.

Contribution

It develops a novel approach that integrates conformal prediction with reachability analysis for safe control in unknown environments, extending prior work to more general dynamical systems.

Findings

Policies achieve strong safety guarantees.

High average rewards maintained.

Validated across diverse control tasks.

Abstract

Designing provably safe control is a core problem in trustworthy autonomy. However, most prior work in this regard assumes either that the system dynamics are known or deterministic, or that the state and action space are finite, significantly limiting application scope. We address this limitation by developing a probabilistic verification framework for unknown dynamical systems which combines conformal prediction with reachability analysis. In particular, we use conformal prediction to obtain valid uncertainty intervals for the unknown dynamics at each time step, with reachability then verifying whether safety is maintained within the conformal uncertainty bounds. Next, we develop an algorithmic approach for training control policies that optimize nominal reward while also maximizing the planning horizon with sound probabilistic safety guarantees. We evaluate the proposed approach in seven safe control settings spanning four domains -- cartpole, lane following, drone control, and safe navigation -- for both affine and nonlinear safety specifications. Our experiments show that the policies we learn achieve the strongest provable safety guarantees while still maintaining high average reward.