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End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks
Open accessAbstract
Reinforcement Learning (RL) algorithms have found limited success beyond simulated applications, and one main reason is the absence of safety guarantees during the learning process. Real world systems would realistically fail or break before an optimal controller can be learned. To address this issue, we propose a controller architecture that combines (1) a model-free RL-based controller with (2) model-based controllers utilizing control barrier functions (CBFs) and (3) online learning of the unknown system dynamics, in order to ensure safety during learning. Our general framework leverages the success of RL algorithms to learn high-performance controllers, while the CBF-based controllers both guarantee safety and guide the learning process by constraining the set of explorable polices. We utilize Gaussian Processes (GPs) to model the system dynamics and its uncertainties. Our novel controller synthesis algorithm, RL-CBF, guarantees safety with high probability during the learning process, regardless of the RL algorithm used, and demonstrates greater policy exploration efficiency. We test our algorithm on (1) control of an inverted pendulum and (2) autonomous carfollowing with wireless vehicle-to-vehicle communication, and show that our algorithm attains much greater sample efficiency in learning than other state-of-the-art algorithms and maintains safety during the entire learning process.
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“Reinforcement learning (RL) algorithms have been increasingly adopted by the robotics community over the past years to control complex robots or multi-robot systems [1], [2], or provide end-to-end policies from perception to control [3].”
From Sim-to-Real Transfer in Deep Reinforcement Learning for Robotics: a Survey (2020) · cites this paper as [3]
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Safe reinforcement learning for wastewater treatment with an input convex safety critic
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BackgroundSEM: Safe exploration mask for q-learning
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Zinage, V., & Bakolas, E. (2023) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc55779.2023.10156243 · Cited by 5
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BackgroundSafety-Aware Unsupervised Skill Discovery
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Lavaei, A., Perez, M., Kazemi, M., Somenzi, F., Soudjani, S., Trivedi, A., & Zamani, M. (2023) · IEEE Open Journal of Control Systems · doi:10.1109/ojcsys.2023.3329394 · Cited by 5
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BackgroundSafe Networked Robotics With Probabilistic Verification
Narasimhan, S. S., Bhat, S., & Chinchali, S. (2023) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2023.3340525 · Cited by 6
“On the other hand, Hamilton-Jacobi reachability analysis [5], [6] and Control Barrier Function methods [7], [8], [30] formulate the safe control problem for the continuous system.”
BackgroundMethodReward Certification for Policy Smoothed Reinforcement Learning
Mu, R., Marcolino, L. S., Zhang, Y., Zhang, T., Huang, X., & Ruan, W. (2024) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v38i19.30139 · Cited by 5
Safety-Critical Learning of Robot Control With Temporal Logic Specifications
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A Review of Safe Online Learning for Nonlinear Control Systems
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FISAR: Forward Invariant Safe Reinforcement Learning with a Deep Neural Network-Based Optimizer
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“Instead of imposing safety constraints on the cumulative cost (see (2)), there is another option of imposing them on individual state-action pairs [15, 16]:”
InfluentialReinforcement Learning Based Distributed Control of Dissipative Networked Systems
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EnergyShield: Provably-Safe Offloading of Neural Network Controllers for Energy Efficiency
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“Recently, Reference [15] developed a CBF-quadratic programming (QP) problem that can compensate for the DRL action such that the compensated action is within a safe set.”
BackgroundDetecting Rewards Deterioration in Episodic Reinforcement Learning
Greenberg, I., & Mannor, S. (2020) · arXiv · doi:10.48550/arxiv.2010.11660 · Cited by 5
Model Free Barrier Functions via Implicit Evading ManeuversPreprint
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“Barrier functions have also been used to guide exploration in [5] via off policy reinforcement learning (RL).”
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Critic as Lyapunov function (CALF): a model-free, stability-ensuring agent
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Q-learning with Long-term Action-space Shaping to Model Complex Behavior for Autonomous Lane Changes
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“Model-free reinforcement learning (or simply reinforcement learning, RL, in what follows) is increasingly used in applications to solve a wide variety of control problems [1–3].”
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Minimum-Variance and Low-Complexity Data-Driven Probabilistic Safe Control Design
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Model-Based Robot Control with Gaussian Process Online Learning: An Experimental Demonstration
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Reducing Safety Interventions in Provably Safe Reinforcement Learning
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MethodRisk-Informed Model-Free Safe Control of Linear Parameter-Varying Systems
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Neural Distributed Controllers with Port-Hamiltonian Structures
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Tutoring Reinforcement Learning via Feedback Control
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BackgroundLearning-Based, Safety-Constrained Control from Scarce Data via Reciprocal Barriers
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Domain-Level Explainability -- A Challenge for Creating Trust in Superhuman AI StrategiesPreprint
Andrulis, J., Meyer, O., Schott, G., Weinbach, S., & Gruhn, V. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2011.06665 · Cited by 7
Provably Correct Training of Neural Network Controllers Using Reachability AnalysisPreprint
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“Such a set of safe actions can be obtained through reachability analysis [19], [20], [21], barrier certificates [22], [23], [24], [25], [26], [27], [28], [29], [30], and online learning of uncertainties [31].”
BackgroundNOVAS: Non-convex Optimization via Adaptive Stochastic Search for End-to-End Learning and ControlPreprint
Exarchos, I., Pereira, M. A., Wang, Z., et al. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.11992 · Cited by 4
“Local 2 optimization modules lead to nested optimization operations, as they interact with the global, end-to-end training of the network that contains them.”
BackgroundSafe Exploration by Solving Early Terminated MDPPreprint
Sun, H., Xu, Z.-P., Fang, M., Peng, Z., Guo, J., Dai, B., & Zhou, B.-L. (2021) · arXiv.org · doi:10.48550/arxiv.2107.04200 · Cited by 27
“[7], Perkins & Barto [25], Chow et al.”
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Lan, X., Huang, Z., Wang, T., Zou, T., & Zhao, Z. (2025) · IEEE Transactions on Consumer Electronics · doi:10.1109/tce.2025.3643855 · Cited by 3
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Cho, M.-J., & Sun, C. (2024) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v38i19.30088 · Cited by 4
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“What’s more, in recent years, CBF has gained popularity in MPC and safe RL methods due to the fact that it ensures the forward invariance of the safe set [22], [23].”
BackgroundReactive Robot Navigation Using Quasi-Conformal Mappings and Control Barrier Functions
Notomista, G., Choi, G. P. T., & Saveriano, M. (2025) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2025.3526377 · Cited by 3
“More recently, safe reinforcement learning problems have been formulated leveraging such a control-theoretic notion of safety [10], [11], [12], [13].”
FORESEE: Prediction With Expansion–Compression Unscented Transform for Online Policy Optimization
Parwana, H., Fang, A., & Panagou, D. (2025) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2025.3572781 · Cited by 3
“Zhang et al. [16] added a safety layer based on control barrier functions (CBFs), and Cheng et al. [17] posed safe reinforcement learning (RL) as a stochastic MPC problem.”
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“…simultaneously by estimating parametric and non-parametric uncertainty based on adaptive CBF [55], robust adaptive CBF [36], Gaussian Process CBF [56], Gaussiance Process robust adaptive CBF [38], disturbance observer-based CBF [57] [58], and several neural network-based CBFs [59] [60] [61].”
Arcos-Legarda, J., Hoyos, A., & Arias, H. F. G. (2025) · Control Theory and Technology · doi:10.1007/s11768-025-00277-3 · Cited by 3
“Reinforcement learning was combined with CBFs to ensure safety during the online learning of unknown system dynamics [17].”
Safety Guided Policy Optimization
Kim, D., Kim, Y., Lee, K., & Oh, S. (2022) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros47612.2022.9981030 · Cited by 3
“Ohnishi et al. [18] and Cheng et al. [19] proposed methods that learn transition models and determine whether a state predicted by the model is safe using a control barrier function.”
BackgrounddSLAP: Distributed Safe Learning and Planning for Multi-robot Systems
Yuan, Z., & Zhu, M. (2022) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc51059.2022.9992938 · Cited by 3
“To the best of our knowledge, this paper is the first to consider extreme scenarios where backup policies are absent, in contrast to [5]–[9].”
Safety-Constrained Policy Transfer with Successor Features
Feng, Z., Zhang, B., Bi, J., & Soh, H. (2023) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra48891.2023.10161256 · Cited by 3
“For example, popular control approaches include the design of Lyapunov functions [15] and barrier functions [16].”
MethodGuiding Reinforcement Learning with Shared Control Templates
Padalkar, A., Quere, G., Steinmetz, F., Raffin, A., Nieuwenhuisen, M., Silvério, J., & Stulp, F. (2023) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra48891.2023.10161058 · Cited by 4
“In [10], Cheng et al. proposed to use Control Barrier Functions (CBFs) [11] to avoid unsafe states for the robot while an RL agent explored the state-action space.”
MethodSafe Reinforcement Learning for Signal Temporal Logic Tasks Using Robust Control Barrier Functions
Chen, J., Zou, Y., & Li, S. (2023) · Chinese Control Conference (CCC) · doi:10.23919/ccc58697.2023.10240080 · Cited by 3
“Researchers have put forth different safety layers based on shielding [8], model predictive safety certification [9], and control barrier functions [10].”
BackgroundSafe Learning-Based Control of Elastic Joint Robots via Control Barrier Functions
Lederer, A., Begzadić, A., Das, N., et al. (2023) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2023.10.1189 · Cited by 3
A Multiplicative Value Function for Safe and Efficient Reinforcement Learning
Bührer, N., Zhang, Z., Liniger, A., Yu, F., & Gool, L. V. (2023) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros55552.2023.10342288 · Cited by 3
“Examples are control barrier functions [35], [36], reachability methods [37], [38] or predictive safe set algorithms [39], [40], [41].”
BackgroundNavigation for autonomous vehicles via fast-stable and smooth reinforcement learning
Zhang, R., Yang, J., Liang, Y., Lu, S., Dong, Y., Yang, B., & Zhang, L. (2023) · Science China Technological Sciences · doi:10.1007/s11431-023-2483-x · Cited by 3
Safe Control Design Through Risk-Tunable Control Barrier Functions
Sharma, V., & Sivaranjani, S. (2023) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc49753.2023.10383233 · Cited by 3
“…to safe control design for systems with uncertainties involves modeling the uncertainty by a known process, with Gaussian Process (GP) models receiving significant attention in typical MPC based control designs [13], [14], as well as CBF-based designs for safety-critical systems [7], [15]–[17].”
BackgroundInfluentialVarricchione, G., Alechina, N., Dastani, M. M., Giacomo, G. D., Logan, B. S., & Perelli, G. (2024) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v38i19.30163 · Cited by 3
“…action replacement , e.g., (Hunt et al. 2021), where unsafe actions are replaced by (default or sampled) safe ones; action projection , e.g., (Cheng et al. 2019), where unsafe actions are replaced by projecting them to the safe action space; and action masking , e.g., (Krasowski, Wang, and…”
Certifiably Robust Reinforcement Learning through Model-Based Abstract Interpretation
Yang, C.-X., Anderson, G., & Chaudhuri, S. (2023) · 2024 IEEE Conference on Secure and Trustworthy Machine Learning (SaTML) · doi:10.1109/satml59370.2024.00018 · Cited by 5
“Reinforcement learning (RL) is an established approach to control tasks [1], [2], including safety-critical ones [3], [4].”
BackgroundConBaT: Control Barrier Transformer for Safe Robot Learning from Demonstrations
Meng, Y., Vemprela, S., Bonatti, R., Fan, C., & Kapoor, A. (2024) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra57147.2024.10611109 · Cited by 6
“[9] use an augmented reward for traffic simulation to guide safe imitation, and we find numerous examples of safe policy design [35], [8], [21], [34].”
BackgroundSafely Learning Dynamical Systems
Ahmadi, A. A., Chaudhry, A., Sindhwani, V., & Tu, S. (2025) · Foundations of Computational Mathematics · doi:10.1007/s10208-025-09689-8 · Cited by 6
Saccani, D., Massai, L., Furieri, L., et al. (2024) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc56724.2024.10886574 · Cited by 3
“These conditions might not hold during exploration, potentially leading to system failures before a safe policy is learned [14].”
Kanso, S., Jha, M., & Theilliol, D. (2025) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc63710.2025.11108023 · Cited by 3
“For example, [2] combines policy-gradient RL with control barrier functions (CBF) to achieve safety, albeit typically requiring nominal models.”
Okawa, Y., Sasaki, T., & Iwane, H. (2020) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2020.12.2198 · Cited by 3
“Dalal et al. (2018) showed a safe exploration method for RL algorithms to satisfy its safety constraints if one-time initial pre-training of a model can be used.”
BackgroundMethodData-driven controller synthesis for abstract systems with regular language specifications
Pola, G., Masciulli, T., Santis, E. D., et al. (2021) · Automatica · doi:10.1016/j.automatica.2021.109903 · Cited by 3
Yu, W., Liu, C. K., & Turk, G. (2021) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra48506.2021.9562051 · Cited by 4
“Some of existing methods enforce the safety of the robot using a model-based approach [9], [10], [23]–[27].”
MethodSafety-Aware Adversarial Inverse Reinforcement Learning for Highway Autonomous Driving
Li, F., Wagner, J. R., & Wang, Y. (2021) · Journal of Autonomous Vehicles and Systems · doi:10.1115/1.4053427 · Cited by 3
Learning-Based Safety-Critical Motion Planning with Input-to-State Barrier Certificate
Jin, X., Jia, Q., Zhang, T., et al. (2021) · 2022 IEEE 18th International Conference on Automation Science and Engineering (CASE) · doi:10.1109/case49439.2021.9551510 · Cited by 3
Zhang, Y., Liang, X., Ge, S. S., et al. (2021) · International Conference on Control, Automation and Systems (ICCAS) · doi:10.23919/iccas52745.2021.9649902 · Cited by 3
Marvi, Z., & Kiumarsi, B. (2021) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc45484.2021.9682839 · Cited by 3
“To deal with dynamic uncertainties in designing safe controllers, [6], [9] have considered a disturbance term in the system dynamics and learned it using a Gaussian process.”
MethodSafe Exploration Method for Reinforcement Learning Under Existence of Disturbance
Okawa, Y., Sasaki, T., Yanami, H., et al. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-26412-2_9 · Cited by 3
Control-Tutored Reinforcement LearningPreprint
Lellis, F. D., Auletta, F., Russo, G., et al. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1912.06085 · Cited by 3
“Reinforcement learning (RL) [1] is increasingly used to learn control policies from data [2]–[4] in applications.”
BackgroundSafe Predictors for Enforcing Input-Output SpecificationsPreprint
Mell, S., Brown, O. M., Goodwin, J. A., & Son, S.-H. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2001.11062 · Cited by 3
Safe Learning of Uncertain EnvironmentsPreprint
Farokhi, F., Leong, A. S., Shames, I., et al. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.01413 · Cited by 3
“Furthermore, without a model, safety often can not be guaranteed during learning but only after a sufficiently long learning period [2], [6], [8].”
BackgroundMethodSafe Exploration for Constrained Reinforcement Learning with Provable Guarantees.Preprint
Bura, A., HasanzadeZonuzy, A., Kalathil, D. M., Shakkottai, S., & Chamberland, J. (2021) · arXiv (Cornell University) · Cited by 3
Learn Zero-Constraint-Violation Policy in Model-Free Constrained Reinforcement LearningPreprint
Ma, H., Liu, C., Li, S. E., et al. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.12953 · Cited by 3
“Nevertheless, it is difficult to find the safe projection, for example, projecting the output to a safe set on the action space [19], or adding a safe layer to the policy network [26].”
InfluentialPhysics-Model-Regulated Deep Reinforcement Learning Towards Safety & Stability Guarantees
Cao, H., Mao, Y., Sha, L., et al. (2023) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc49753.2023.10383560 · Cited by 2
“Given the desired safety specification, one can also leverage control barrier function [5], [14], [16] and reachability analysis [15] to certify the control command to satisfy the safety requirement.”
BackgroundMethodInfluentialDey, S., & Xu, H. (2024) · Neural Computing and Applications · doi:10.1007/s00521-024-10639-8 · Cited by 2
“Two distinct approaches for state constraint-set certification are the control barrier function (CBF) method [10–12] and the Hamilton-Jacobi reachability [13–15] analysis.”
Metadata
- Authors
- Cheng, R., Orosz, G., Murray, R. M., & Burdick, J. W.
- Affiliations
- California Institute of Technology (US)
- University of Michigan (US)
- Venue
- Proceedings of the AAAI Conference on Artificial Intelligence
- Published
- 2019-07-17
- Volume
- 33
- Issue
- 01
- Pages
- 3387-3395
- ISSN
- 2159-5399 (ISSN-L)
- 2374-3468
- OpenAlex
- W2966735560
- Semantic Scholar
- adcd4bfd88213da0c33d3cb7057411dd15b72c7a
- Cited by
- 611
- References
- 34
- Citations by year
- 2026: 79 · 2025: 84 · 2024: 79 · 2023: 102 · 2022: 84 · 2021: 112 · 2020: 60 · 2019: 10
- FWCI
- 25.44
- Type
- conference paper
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- www.aaai.org/ (unspecified)
- Locations
- Proceedings of the AAAI Conference on Artificial Intelligence (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- AAAI Publications (The Association for the Advancement of Artificial Intelligence (AAAI)) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Reinforcement Learning in Robotics
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Dynamic Programming Control
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Formal Methods in Verification
- Keywords
- safe reinforcement learning, control barrier functions, safety-critical control, continuous control, model-based control, policy exploration, sample efficiency, inverted pendulum, vehicle-to-vehicle communication
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