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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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Citations
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Lyapunov-Inspired Deep Reinforcement Learning for Robot Navigation in Obstacle Environments
Uğurlu, H. İ., Redder, A., & Kayacan, E. (2025) · IEEE Symposium on Computational Intelligence for Engineering Solutions (CIES) · doi:10.1109/cies64955.2025.11007627 · Cited by 2
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Autonomous Operations With a Safe Reinforcement Learning Approach for Urban Rail Transit
Zhao, Z., Xun, J., Lin, Y., Chow, A. H. F., & Chen, J. (2025) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2025.3588585 · Cited by 2
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Safe Uncertainty-Aware Learning Framework for Robotic Suturing
Empleo, W. P., Kim, Y., Kim, H., Savarimuthu, T. R., & Iturrate, I. (2025) · IEEE Transactions on Medical Robotics and Bionics · doi:10.1109/tmrb.2025.3646752 · Cited by 3
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Learning to be safe, in finite time
Castellano, A., Bazerque, J. A., & Mallada, E. (2021) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc50511.2021.9482829 · Cited by 2
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BackgroundTowards Explainability in Modular Autonomous System Software
Zheng, H., Zang, Z., Yang, S., & Mangharam, R. (2023) · IEEE Intelligent Vehicles Symposium · doi:10.1109/iv55152.2023.10186720 · Cited by 2
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Osinenko, P., Yaremenko, G., Malaniya, G., & Bolychev, A. (2023) · IEEE Access · doi:10.1109/access.2023.3306070 · Cited by 3
“Another application of control barrier functions is due to [98], where a safe controller was coupled with amodel-free reinforcement learning agent.”
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“To achieve safe policy optimization, control barrier functions (CBFs) have been widely explored [6], [7], [11], [12], [13], which keep the system evolving inside a safe invariant set.”
Wu, M., Yu, F. R., & Liu, P. X. (2024) · IEEE Transactions on Vehicular Technology · doi:10.1109/tvt.2024.3398661 · Cited by 2
“For learning iteration [0,20], the baseline VFDT achieves better prediction accuracy than our proposed approach for label unsafe.”
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Jha, M., Kiumarsi, B., & Theilliol, D. (2024) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc60939.2024.10644965 · Cited by 2
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Primal-Dual Multi-Agent Trust Region Policy Optimization for Safe Multi-Agent Reinforcement Learning
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A Reinforcement Learning-Based Double Layer Controller for Mobile Robot in Human-Shared Environments
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Safe and Efficient CAV Lane Changing using Decentralised Safety Shields
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“…set C is forward invariant if the function h is a Control Barrier Function (CBF) such that there exists η ∈ [0 , 1] for all s t ∈ C satisfying the following equation where η is the coefficient of zero order control that defines the magnitude at which the system is pushed within the safe set C [13].”
InfluentialHan, D., & Huang, H. (2022) · Asian Control Conference (ASCC) · doi:10.23919/ascc56756.2022.9828315 · Cited by 2
“Reinforcement learning approaches have obtained a safe exploration inside the ROA [16]–[18] and data-driven learning approaches can provide a rich set of control options at a certain level of probability [19], [20].”
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Song, L., Ferderer, L., & Wu, S. (2022) · International Conference on Machine Learning and Applications · doi:10.1109/icmla55696.2022.00045 · Cited by 2
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BackgroundMethodLearning Safety Filters for Unknown Discrete-Time Linear Systems
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Chekan, J. A., & Langbort, C. (2023) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc55779.2023.10156490 · Cited by 2
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Lin, X., Koochakzadeh, A., Yazıcıoğlu, Y., et al. (2023) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros55552.2023.10342259 · Cited by 2
“For example, control barrier function can be adopted to ensure safety during reinforcement learning by constraining the exploration set [3] or augmenting the cost function [4].”
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Compactly Restrictable Metric Policy Optimization Problems
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Safe Reinforcement Learning for Grid Voltage ControlPreprint
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Safe Value Functions: Learned Critics as Hard Safety Constraints
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Enhancing Safety in Model‐Based Reinforcement Learning With High‐Order Control Barrier Functions
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RAIL: Recursive A* and Imitation Learning-Based Approach for Collision-Free Path Estimation
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InfluentialSafe Reinforcement Learning with Constraints: A Survey
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Region-Driven Adaptation for Constrained Reinforcement Learning-Based Control
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“Restrictions apply. transition for MDP [5] and this has no effect on the safety-critical control design presented in Section IV.”
InfluentialKalaria, D., Lin, Q., & Dolan, J. M. (2025) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros60139.2025.11246408 · Cited by 4
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Reinforcement learning–based safety control strategy for mixed vehicle platoons
Zhou, J., Deng, H., Wu, J., et al. (2025) · Transactions of the Institute of Measurement and Control · doi:10.1177/01423312251392309 · Cited by 1
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Curriculum Reinforcement Learning for Fuel-Optimal Spacecraft Guidance and Control with Constraints
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“Most widely used approaches are projection-based, including Control Barrier Functions (CBFs) [1], [4], [6], [18] and Safety Predictive Filters (SPFs) [25], which explicitly enforce safety by projecting the nominal action onto an admissible set [15].”
Adaptive Control Algorithms for Pure-Feedback Plants Based on the Reinforcement Learning Method
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Safe Reinforcement Learning for Nonlinear Multiagent Systems Based on Min--Max DMPC
Peng, Y., Yan, H., Liu, Q., et al. (2026) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2026.3679663 · Cited by 1
“The third approach focuses on intrinsic safety guarantees [37], [38], [39], [40], [41], [42].”
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Wu, Y. N., Tian, S., Tao, W., Ji, Z., & Wei, C. (2026) · IEEE Internet of Things Journal · doi:10.1109/jiot.2026.3709862 · Cited by 1
“If unsafe behaviors are constrained only through indirect reward penalties, DRL policies may fail to provide timely and reliable safety guarantees in complex dynamic scenarios [19].”
SEO: Safety-Aware Energy Optimization Framework for Multi-Sensor Neural Controllers at the Edge
Odema, M., Ferlez, J., Shoukry, Y., et al. (2023) · Proceedings - ACM IEEE Design Automation Conference · doi:10.1109/dac56929.2023.10247751 · Cited by 1
“Whereas another leverages control theory concepts to augment NN controllers with formal safety guarantees on their outputs, filtering them and applying necessary corrections if needed [16], [17].”
BackgroundA Safety Filter for Realizing Safe Robot Navigation in Crowds
Feng, K., Lu, Z., Xu, J., et al. (2023) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros55552.2023.10342054 · Cited by 1
“Cheng et al. [15] developed a safe reinforcement learning framework that combines CBFs with model-free reinforcement learning.”
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Zou, J., Zhang, S., & Qiu, M. (2024) · Lecture notes in computer science · doi:10.1007/978-981-97-5498-4_14 · Cited by 1
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Zhao, Y., Mao, J., & Zhang, C. (2025) · International Conference on Automation, Control and Robotics Engineering (CACRE) · doi:10.1109/cacre66141.2025.11119610 · Cited by 1
“…u CBFk ( s, u RLθ k ) , which is influenced by the RL-based control, is formulated as the following QP problem: ) Specifically, the result of Lemma 1 in [14] can be extended to (11), where ϵ max = max s ∈X denotes the maximum barrier violation in (11), i.e., the largest deviation from safety.”
One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environments
Lin, A., Peng, S., & Bansal, S. (2025) · IEEE Transactions on Robotics · doi:10.1109/tro.2025.3644957 · Cited by 16
“To address these shortcomings, recent works have explored safety critics and backup policies to safeguard RL-based controllers [23], [24], [25], [26], [27], [28], [29], [30].”
InfluentialMarthi, S., Jha, M., Kanso, S., et al. (2025) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc57313.2025.11312958 · Cited by 1
“35 and f η = [1 , 3 , 7 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , 31 , 33] .”
Barrier-certified Learning-based Control of Systems with Uncertain Safe Set
Marvi, Z., & Kiumarsi, B. (2021) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc50511.2021.9483332 · Cited by 1
Improving deep reinforcement learning by safety guarding model via hazardous experience planning
Peng, P., Zhu, F., Ling, X., et al. (2021) · Frontiers of Computer Science · doi:10.1007/s11704-021-0250-y · Cited by 1
An actor-critic strategy for a safe and efficient human robot collaboration
Gabrielli, G., & Secchi, C. (2021) · International Conference on Advanced Robotics (ICAR) · doi:10.1109/icar53236.2021.9659462 · Cited by 1
Enforcing Hard State-Dependent Action Bounds on Deep Reinforcement Learning Policies
Cooman, B. D., Suykens, J. A. K., & Ortseifen, A. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-25891-6_16 · Cited by 1
Control-Tutored Reinforcement Learning: an application to the Herding ProblemPreprint
Lellis, F. D., Auletta, F., Russo, G., et al. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1911.11444 · Cited by 1
“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 (Kober et al., 2013; Garcıa and Fernández, 2015; Cheng et al., 2019).”
BackgroundArasanipalai, R., Agrawal, A., & Ghose, D. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2002.11564 · Cited by 2
$\mathcal{L}_1$-$\mathcal{GP}$: $\mathcal{L}_1$ Adaptive Control with Bayesian LearningPreprint
Gahlawat, A., Zhao, P., Patterson, A., et al. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2004.14594 · Cited by 1
“When the learning methods generate unsafe reference/control commands, the control barrier function methods presented by Cheng et al. (2019), Salehi et al. (2019), and Taylor and Ames (2019) correct the control input to ensure the system state remains in a safe set.”
MethodLearning Control Barrier Functions with High Relative Degree for Safety-Critical ControlPreprint
Wang, C., Li, Y., Meng, Y., et al. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2011.10721 · Cited by 1
“The authors in [7] also use Gaussian process to estimate the model but focusing on the safety during the training process.”
MethodSafety-Constrained Learning and Control using Scarce Data and Reciprocal BarriersPreprint
Verginis, C. K., Djeumou, F., & Topcu, U. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2105.06526 · Cited by 1
“Barrier certificates have also been integrated with learning-based approaches to address the safety of uncertain systems [8], [28]–[33]; [28]–[30], however, only consider additive uncertain terms modeled by Gaussian processes and assumed to evolve in compact sets.”
BackgroundFast and Safe Trajectory Optimization for Autonomous Mobile Robots using Reachability Analysis
Vaskov, S. (2021) · Deep Blue (University of Michigan) · doi:10.7302/2774 · Cited by 1
Credit Assignment Safety Learning from Human DemonstrationsPreprint
Prabhakar, A., & Billard, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2110.04633 · Cited by 1
“2016, 2019), shared control (Zhang, Yang, and Khurshid 2020), and reinforcement learning (Cheng et al. 2019).”
BackgroundSafe Learning of Linear Time-Invariant Systems.Preprint
Farokhi, F., Leong, A. S., Zamani, M. R., et al. (2021) · arXiv (Cornell University) · Cited by 1
Padalkar, A., Quere, G., Raffin, A., Silvério, J., & Stulp, F. (2023) · Research Square · doi:10.21203/rs.3.rs-3289569/v1 · Cited by 1
A Survey of Machine-Learning-Based Scheduling: From Solver-Centric to Data-Centric ParadigmsPreprint
Liu, A., Lin, S., Chen, J., Wu, P., & Shen, Z. M. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.5974954 · Cited by 1
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)
Set-Invariant Constrained Reinforcement Learning with a Meta-Optimizer.Preprint
Sun, C., Kim, D. K., & How, J. P. (2020) · arXiv (Cornell University)
Xi, F., & Xuejun, R. (2020) · International Conference on Electronics and Sustainable Communication Systems (ICESC) · doi:10.1109/icesc48915.2020.9155781
FISAR: Forward Invariant Safe Reinforcement Learning with a Deep Neural Network-Based OptimizePreprint
Sun, C., Kim, D.-K., & How, J. P. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.11419
“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]:”
InfluentialAssured RL: Reinforcement Learning with Almost Sure ConstraintsPreprint
Castellano, A., Bazerque, J. A., & Mallada, E. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2012.13036
“, 2019), and methods with additional assumptions on the model (Zanon and Gros, 2019; Cheng et al., 2019).”
MethodLiu, K., Li, N., Kolmanovsky, I. V., et al. (2021) · arXiv (Cornell University)
Learning Deep Neural Policies with Stability GuaranteesPreprint
Khader, S. A., Yin, H., Falco, P., & Kragić, D. (2021) · arXiv (Cornell University)
Failing with Grace: Learning Neural Network Controllers that are Boundedly UnsafePreprint
Vlantis, P., Bridgeman, L. J., & Zavlanos, M. M. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2106.11881
“Compared to the methods in [10, 11, 13] that employ”
MethodInfluentialNeural Network Repair with Reachability AnalysisPreprint
Yang, X.-D., Yamaguchi, T., Tran, H.-D., Hoxha, B., Johnson, T. T., & Prokhorov, D. (2021) · International Conference on Formal Modeling and Analysis of Timed Systems · doi:10.48550/arxiv.2108.04214 · Cited by 38
“There is significant recent work on safe RL [Alshiekh et al. 2018; Bouton et al. 2019; Cheng et al. 2019; Fulton and Platzer 2018; Huang et al. 2020; Islam et al. 2020; Sohn et al. 2019b; Xiong et al. 2020; Zhou et al. 2020].”
Dependability Analysis of Deep Reinforcement Learning based Robotics and Autonomous Systems.Preprint
Dong, Y., Zhao, X., & Huang, X. (2021) · arXiv (Cornell University)
Safety-aware Policy Optimisation for Autonomous RacingPreprint
Chen, B., Francis, J., Herman, J., Oh, J., Nyberg, E., & Herbert, S. (2021) · arXiv (Cornell University) · doi:10.13140/rg.2.2.19310.13125
Assured Multi-agent Reinforcement Learning with Robust Agent-Interaction Adaptability
Riley, J., Călinescu, R., Paterson, C., et al. (2022) · Smart innovation, systems and technologies · doi:10.1007/978-981-19-3444-5_8
Learning safe behaviour via justified human preferences and hypothetical queries
Kazantzidis, I., Norman, T. J., Du, Y., & Freeman, C. T. (2026) · Autonomous Agents and Multi-Agent Systems · doi:10.21203/rs.3.rs-2406802/v1 · Cited by 1
Farokhi, F., Leong, A. S., Shames, I., et al. (2023) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc55779.2023.10156091
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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