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Conformal Reachability for Safe Control in Unknown Environments

Xinhang Ma, Junlin Wu, Yiannis Kantaros, Yevgeniy Vorobeychik

TL;DR

This work introduces ReCORS, a framework that achieves provable safety for reinforcement learning in unknown dynamical environments by uniting conformal prediction with finite-horizon reachability. It learns a surrogate dynamics model and a differentiable conformal safety module to provide trajectory-level uncertainty sets, enabling verified safety guarantees with a controllable confidence level while still pursuing high rewards via model-free RL. The approach blends model-based learning with model-free optimization, and introduces differentiable conformal and safety losses to enable end-to-end training. Empirical results across seven safe-control tasks show ReCORS attaining state-of-the-art safety guarantees with competitive or superior rewards, highlighting its potential for trustworthy autonomy in uncertain environments.

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.

Conformal Reachability for Safe Control in Unknown Environments

TL;DR

This work introduces ReCORS, a framework that achieves provable safety for reinforcement learning in unknown dynamical environments by uniting conformal prediction with finite-horizon reachability. It learns a surrogate dynamics model and a differentiable conformal safety module to provide trajectory-level uncertainty sets, enabling verified safety guarantees with a controllable confidence level while still pursuing high rewards via model-free RL. The approach blends model-based learning with model-free optimization, and introduces differentiable conformal and safety losses to enable end-to-end training. Empirical results across seven safe-control tasks show ReCORS attaining state-of-the-art safety guarantees with competitive or superior rewards, highlighting its potential for trustworthy autonomy in uncertain environments.

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.
Paper Structure (30 sections, 1 theorem, 27 equations, 6 figures, 1 table, 1 algorithm)

This paper contains 30 sections, 1 theorem, 27 equations, 6 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Deep Reinforcement Learning
  5. Conformal Prediction
  6. Model
  7. Solution Approach
  8. Learning System Dynamics with Safety Specifications
  9. Conformal Safety Analysis
  10. Training with Differentiable Conformal and Safety Loss
  11. Conformal Loss
  12. Safety Loss
  13. Putting Everything Together: The ReCORS Algorithm
  14. Experiments
  15. Experiment Setup
  16. ...and 15 more sections

Key Result

Theorem 1

Let $\{s_0^i\}_{i=1}^N$ be i.i.d. samples from $\rho$, independent of the calibration data used to construct the conformal bounds. Suppose the conformal procedure provides a trajectory-level coverage guarantee that for every fixed initial state $s_0$, $\Pr\!(S(s_0;\pi_\theta)\cap\mathcal{S}_u=\empty

Figures (6)

  • Figure 1: Probabilistic safety verification results. Higher is better. ReCORS-UB (red solid line) is applying conformal prediction per-step and union bounding the results. ReCORS-TS (pink dotted line) uses the time series conformal prediction method from cleaveland2024conformal. All the baseline plotted lines use the conformal prediction method that results in better verified safety results.
  • Figure 2: Empirical safety evaluation, comparing safety cost ReCORS (red line) with baselines. Lower is better.
  • Figure 3: Verified safety (left) and empirical safety (right) for 2D Quadrotor with nonlinear safe distance constraint.
  • Figure 4: Reward comparisons of ReCORS (red line) with baselines. Higher is better.
  • Figure 5: Reward comparisons in 2D Quadrotor environment with nonlinear safe distance constraint.
  • ...and 1 more figures

Theorems & Definitions (1)

  • Theorem 1