# End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functions

arXiv: https://arxiv.org/abs/2212.11365 · HTML: https://mlsanity.com/paper/2212.11365/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Safe offline RL, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 21 Dec 2022.

## Placed in

- Offline RL and imitation learning from data / [Safe offline RL](https://mlsanity.com/offlinerl/safe-offline-rl/)

## Builds on (most cited first, 20 of 20)

- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [End-to-end Driving via Conditional Imitation Learning](https://mlsanity.com/paper/1710.02410/) (2017)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [A predictive safety filter for learning-based control of constrained nonlinear dynamical systems](https://mlsanity.com/paper/1812.05506/) (2018)
- [Learning for Safety-Critical Control with Control Barrier Functions](https://mlsanity.com/paper/1912.10099/) (2019)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [Linear model predictive safety certification for learning-based control](https://mlsanity.com/paper/1803.08552/) (2018)
- [Imitation Learning with Stability and Safety Guarantees](https://mlsanity.com/paper/2012.09293/) (2020)
- [Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functions](https://mlsanity.com/paper/2010.16001/) (2020)
- [Risk-Aware Active Inverse Reinforcement Learning](https://mlsanity.com/paper/1901.02161/) (2019)
- [Input-to-State Safety With Control Barrier Functions](https://mlsanity.com/paper/1803.03035/) (2018)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [Training Neural Network Controllers Using Control Barrier Functions in the Presence of Disturbances](https://mlsanity.com/paper/2001.08088/) (2020)
- [Model-Free Safety-Critical Control for Robotic Systems](https://mlsanity.com/paper/2109.09047/) (2021)
- [Autonomous Racing using Learning Model Predictive Control](https://mlsanity.com/paper/1610.06534/) (2016)
- [Episodic Learning for Safe Bipedal Locomotion with Control Barrier Functions and Projection-to-State Safety](https://mlsanity.com/paper/2105.01697/) (2021)
- [Safety-Aware Preference-Based Learning for Safety-Critical Control](https://mlsanity.com/paper/2112.08516/) (2021)
- [Safe Controller Synthesis with Tunable Input-to-State Safe Control Barrier Functions](https://mlsanity.com/paper/2103.08041/) (2021)
- [Characterizing Safety: Minimal Barrier Functions from Scalar Comparison Systems](https://mlsanity.com/paper/1908.09323/) (2019)

## Built on by (most cited first, 10 of 10)

- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [SAFE-GIL: SAFEty Guided Imitation Learning for Robotic Systems](https://mlsanity.com/paper/2404.05249/) (2024)
- [Constrained Diffusers for Safe Planning and Control](https://mlsanity.com/paper/2506.12544/) (2025)
- [Imitation Learning from Nonlinear MPC via the Exact Q-Loss and its Gauss-Newton Approximation](https://mlsanity.com/paper/2304.01782/) (2023)
- [A Simple Approach to Constraint-Aware Imitation Learning with Application to Autonomous Racing](https://mlsanity.com/paper/2503.07737/) (2025)
- [Online Efficient Safety-Critical Control for Mobile Robots in Unknown Dynamic Multi-Obstacle Environments](https://mlsanity.com/paper/2402.16449/) (2024)
- [Approximate Model Predictive Control for Microgrid Energy Management via Imitation Learning](https://mlsanity.com/paper/2510.20040/) (2025)
- [RISE: Robust Imitation through Stochastic Encoding](https://mlsanity.com/paper/2503.12243/) (2025)
- [Safety-Guaranteed Imitation Learning from Nonlinear Model Predictive Control for Spacecraft Close Proximity Operations](https://mlsanity.com/paper/2603.18910/) (2026)
- [Infeasible optimization problems and the hierarchical augmented Lagrangian method in imitation learning](https://mlsanity.com/paper/2606.00730/) (2026)

## Abstract (arXiv)

Imitation learning (IL) is a learning paradigm which can be used to synthesize controllers for complex systems that mimic behavior demonstrated by an expert (user or control algorithm). Despite their popularity, IL methods generally lack guarantees of safety, which limits their utility for complex safety-critical systems. In this work we consider safety, formulated as set-invariance, and the associated formal guarantees endowed by Control Barrier Functions (CBFs). We develop conditions under which robustly-safe expert controllers, utilizing CBFs, can be used to learn end-to-end controllers (which we refer to as CBF-Compliant controllers) that have safety guarantees. These guarantees are presented from the perspective of input-to-state safety (ISSf) which considers safety in the context of disturbances, wherein it is shown that IL using robustly safe expert demonstrations results in ISSf with the disturbance directly related to properties of the learning problem. We demonstrate these safety guarantees in simulated vision-based end-to-end control of an inverted pendulum and a car driving on a track.