# Statistically Assuring Safety of Control Systems using Ensembles of Safety Filters and Conformal Prediction

arXiv: https://arxiv.org/abs/2511.07899 · HTML: https://mlsanity.com/paper/2511.07899/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 21 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 16 of 16)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [End-to-end Autonomous Driving: Challenges and Frontiers](https://mlsanity.com/paper/2306.16927/) (2023)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis](https://mlsanity.com/paper/2502.00935/) (2025)
- [Uncertainty-aware Latent Safety Filters for Avoiding Out-of-Distribution Failures](https://mlsanity.com/paper/2505.00779/) (2025)
- [Run Time Assurance for Safety-Critical Systems: An Introduction to Safety Filtering Approaches for Complex Control Systems](https://mlsanity.com/paper/2110.03506/) (2021)
- [Formal Verification and Control with Conformal Prediction](https://mlsanity.com/paper/2409.00536/) (2024)
- [Verification of Neural Reachable Tubes via Scenario Optimization and Conformal Prediction](https://mlsanity.com/paper/2312.08604/) (2023)
- [Conformal Predictive Safety Filter for RL Controllers in Dynamic Environments](https://mlsanity.com/paper/2306.02551/) (2023)
- [Certifiable Reachability Learning Using a New Lipschitz Continuous Value Function](https://mlsanity.com/paper/2408.07866/) (2024)
- [Designing Latent Safety Filters using Pre-Trained Vision Models](https://mlsanity.com/paper/2509.14758/) (2025)
- [Safe Decentralized Multi-Agent Control using Black-Box Predictors, Conformal Decision Policies, and Control Barrier Functions](https://mlsanity.com/paper/2409.18862/) (2024)
- [Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functions](https://mlsanity.com/paper/2505.11755/) (2025)

## Built on by (most cited first, 4 of 4)

- [Safe Control using Learned Safety Filters and Adaptive Conformal Inference](https://mlsanity.com/paper/2604.18482/) (2026)
- [Reliability-Asymmetric Spacecraft Autonomy: Co-Designing a Capable Learned GNC Stack with a Verified, Adaptation-Aware Runtime Shield](https://mlsanity.com/paper/2606.25366/) (2026)
- [Conformal Recovery-Deadline Certificates for Runtime Assurance of Adapting Controllers](https://mlsanity.com/paper/2606.25371/) (2026)
- [CrossSafe: Towards Cross-Embodiment Latent Safety Filters](https://mlsanity.com/paper/2609.28984/) (2026)

## Abstract (arXiv)

Safety assurance is a fundamental requirement for deploying learning-enabled autonomous systems. Hamilton-Jacobi (HJ) reachability analysis is a fundamental method for formally verifying safety and generating safe controllers. However, computing the HJ value function that characterizes the backward reachable set (BRS) of a set of user-defined failure states is computationally expensive, especially for high-dimensional systems, motivating the use of reinforcement learning approaches to approximate the value function. Unfortunately, a learned value function and its corresponding safe policy are not guaranteed to be correct. The learned value function evaluated at a given state may not be equal to the actual safety return achieved by following the learned safe policy. To address this challenge, we introduce a conformal prediction-based (CP) framework that bounds such uncertainty. We leverage CP to provide probabilistic safety guarantees when using learned HJ value functions and policies to prevent control systems from reaching failure states. Specifically, we use CP to calibrate the switching between the unsafe nominal controller and the learned HJ-based safe policy and to derive safety guarantees under this switched policy. We also investigate using an ensemble of independently trained HJ value functions as a safety filter and compare this ensemble approach to using individual value functions alone.