mlsanityData to 7 Oct 2026

Learning Control Barrier Functions from Expert Demonstrations

arXiv 2004.03315 ↗First posted 7 Apr 2020eess.SY cs.LG cs.SYcited by 88

On the map: Offline RL and imitation learning from data → Safe offline RL

Abstract (arXiv)

Inspired by the success of imitation and inverse reinforcement learning in replicating expert behavior through optimal control, we propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs). We consider the setting of a known nonlinear control affine dynamical system and assume that we have access to safe trajectories generated by an expert - a practical example of such a setting would be a kinematic model of a self-driving vehicle with safe trajectories (e.g., trajectories that avoid collisions with obstacles in the environment) generated by a human driver. We then propose and analyze an optimization-based approach to learning a CBF that enjoys provable safety guarantees under suitable Lipschitz smoothness assumptions on the underlying dynamical system. A strength of our approach is that it is agnostic to the parameterization used to represent the CBF, assuming only that the Lipschitz constant of such functions can be efficiently bounded. Furthermore, if the CBF parameterization is convex, then under mild assumptions, so is our learning process. We end with extensive numerical evaluations of our results on both planar and realistic examples, using both random feature and deep neural network parameterizations of the CBF. To the best of our knowledge, these are the first results that learn provably safe control barrier functions from data.

Key facts. Cited by 88 papers in the map (data through 7 Oct 2026). Placed in Safe offline RL, one of 13 directions in Offline RL and imitation learning from data. First posted on arXiv 7 Apr 2020.

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Citing papers per year: 2021: 16; 2022: 13; 2023: 10; 2024: 14; 2025: 19; 2026: 16.

88 papers.

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  1. 2023The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systemscited by 77
  2. 2021Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificatescited by 71
  3. 2023SafeDiffuser: Safe Planning with Diffusion Probabilistic Modelscited by 69
  4. 2024Safe Offline Reinforcement Learning with Feasibility-Guided Diffusion Modelcited by 62
  5. 2025Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysiscited by 44
  6. 2025Safety Guardrails for LLM-Enabled Robotscited by 30
  7. 2025Uncertainty-aware Latent Safety Filters for Avoiding Out-of-Distribution Failurescited by 30
  8. 2022Lyapunov Density Models: Constraining Distribution Shift in Learning-Based Controlcited by 28
  9. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  10. 2022Safe Control Under Input Limits with Neural Control Barrier Functionscited by 27
  11. 2021Safe Pontryagin Differentiable Programmingcited by 25
  12. 2021Safe Occlusion-aware Autonomous Driving via Game-Theoretic Active Perceptioncited by 22
38 more
  1. 2022Safety Certification for Stochastic Systems via Neural Barrier Functionscited by 22
  2. 2025Steering Dialogue Dynamics for Robustness against Multi-turn Jailbreaking Attackscited by 20
  3. 2021Learning Robust Output Control Barrier Functions from Safe Expert Demonstrationscited by 19
  4. 2021Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximationcited by 16
  5. 2023In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution Statescited by 15
  6. 2021Learning Robust Hybrid Control Barrier Functions for Uncertain Systemscited by 14
  7. 2023Active Uncertainty Reduction for Safe and Efficient Interaction Planning: A Shielding-Aware Dual Control Approachcited by 13
  8. 2021SHARP: Shielding-Aware Robust Planning for Safe and Efficient Human-Robot Interactioncited by 12
  9. 2024Safe Reinforcement Learning on the Constraint Manifold: Theory and Applicationscited by 12
  10. 2024Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imaginationcited by 12
  11. 2021BarrierNet: A Safety-Guaranteed Layer for Neural Networkscited by 11
  12. 2022Joint Differentiable Optimization and Verification for Certified Reinforcement Learningcited by 11
  13. 2025SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functionscited by 11
  14. 2022Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Drivingcited by 10
  15. 2022Temporal Logic Imitation: Learning Plan-Satisficing Motion Policies from Demonstrationscited by 10
  16. 2023Online Control Barrier Functions for Decentralized Multi-Agent Navigationcited by 10
  17. 2022Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environmentscited by 8
  18. 2023Sequential Neural Barriers for Scalable Dynamic Obstacle Avoidancecited by 8
  19. 2021Safe Value Functionscited by 7
  20. 2024Verification-Aided Learning of Neural Network Barrier Functions with Termination Guaranteescited by 7
  21. 2026Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPUcited by 7
  22. 2025Two-Stage Learning of Stabilizing Neural Controllers via Zubov Sampling and Iterative Domain Expansioncited by 6
  23. 2021Provably Correct Training of Neural Network Controllers Using Reachability Analysiscited by 5
  24. 2024MAGICS: Adversarial RL with Minimax Actors Guided by Implicit Critic Stackelberg for Convergent Neural Synthesis of Robot Safetycited by 5
  25. 2025V-OCBF: Learning Safety Filters from Offline Data via Value-Guided Offline Control Barrier Functionscited by 5
  26. 2024Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuationcited by 4
  27. 2024Reinforcement Learning with Ensemble Model Predictive Safety Certificationcited by 4
  28. 2025CP-NCBF: A Conformal Prediction-based Approach to Synthesize Verified Neural Control Barrier Functionscited by 4
  29. 2025Learning Conservative Neural Control Barrier Functions from Offline Datacited by 4
  30. 2021Model Free Barrier Functions via Implicit Evading Maneuverscited by 3
  31. 2021Learning Contraction Policies from Offline Datacited by 3
  32. 2022Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Modelscited by 3
  33. 2022Safe Inverse Reinforcement Learning via Control Barrier Functioncited by 3
  34. 2023Multi-Step Model Predictive Safety Filters: Reducing Chattering by Increasing the Prediction Horizoncited by 3
  35. 2024Learning safety critics via a non-contractive binary bellman operatorcited by 3
  36. 2024Learning Control Barrier Functions and their application in Reinforcement Learning: A Surveycited by 3
  37. 2024Compositional Curvature Bounds for Deep Neural Networkscited by 3
  38. 2025Estimating Control Barriers from Offline Datacited by 3

50 most cited of 88 All 88 (JSON)

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  1. 2022End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functions
  2. 2020Training Neural Network Controllers Using Control Barrier Functions in the Presence of Disturbances
  3. 2025Barrier Function Overrides For Non-Convex Fixed Wing Flight Control and Self-Driving Cars
  4. 2023Safe Neural Control for Non-Affine Control Systems with Differentiable Control Barrier Functions
  5. 2024Semi-Supervised Safe Visuomotor Policy Synthesis using Barrier Certificates
  6. 2022Safe Reinforcement Learning with Probabilistic Control Barrier Functions for Ramp Merging
  7. 2026Individual Control Barrier Functions-Guided Diffusion Model for Safe Offline Multi-Agent Reinforcement Learning
  8. 2023Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Models