{"type":"ScholarlyArticle","title":"State-wise Safe Reinforcement Learning: A Survey","authors":[{"name":"Weiye Zhao","slug":"weiye-zhao","given":"Weiye","family":"Zhao","affiliation":"Robotics Institute , Carnegie Mellon University"},{"name":"Tairan He","slug":"tairan-he","given":"Tairan","family":"He","affiliation":"Robotics Institute , Carnegie Mellon University"},{"name":"Rui Chen","slug":"rui-chen","given":"Rui","family":"Chen","affiliation":"Robotics Institute , Carnegie Mellon University"},{"name":"Tianhao Wei","slug":"tianhao-wei","given":"Tianhao","family":"Wei","affiliation":"Robotics Institute , Carnegie Mellon University"},{"name":"Changliu Liu","slug":"changliu-liu","given":"Changliu","family":"Liu","affiliation":"Robotics Institute , Carnegie Mellon University"}],"abstract":"Despite the tremendous success of Reinforcement Learning (RL) algorithms in simulation environments, applying RL to real-world applications still faces many challenges. A major concern is safety, in another word, constraint satisfaction. State-wise constraints are one of the most common constraints in real-world applications and one of the most challenging constraints in Safe RL. Enforcing state-wise constraints is necessary and essential to many challenging tasks such as autonomous driving, robot manipulation. This paper provides a comprehensive review of existing approaches that address state-wise constraints in RL. Under the framework of State-wise Constrained Markov Decision Process (SCMDP), we will discuss the connections, differences, and trade-offs of existing approaches in terms of (i) safety guarantee and scalability, (ii) safety and reward performance, and (iii) safety after convergence and during training. We also summarize limitations of current methods and discuss potential future directions.","doi":"10.24963/ijcai.2023/763","url":"https://ijcai.org/proceedings/2023/763","pdf":"https://ijcai.org/proceedings/2023/0763.pdf","markdown":"https://ijcai.org/proceedings/2023/763.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/763","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Survey Track","track":"Survey Track","number":763,"pages":{"first":6814,"last":6822},"keywords":["Survey: Constraint Satisfaction and Optimization","Survey: Robotics","Survey: Machine Learning"],"videos":[],"references":[{"position":1,"raw":"[Achiam et al., 2017] Joshua Achiam, David Held, Aviv Tamar, and Pieter Abbeel. Constrained policy optimiza- tion. In International Conference on Machine Learning, pages 22-31. PMLR, 2017.","title":"Constrained policy optimization","authors":"Achiam","year":"2017","venue":"International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Ames et al., 2014] Aaron D Ames, Jessy W Grizzle, and Paulo Tabuada. Control barrier function based quadratic programs with application to adaptive cruise control. In 53rd IEEE Conference on Decision and Control, pages 6271-6278. IEEE, 2014.","title":"Control barrier function based quadratic programs with application to adaptive cruise control","authors":"Jessy W Aaron D Ames, Paulo Grizzle, Tabuada","year":"2014","venue":"53rd IEEE Conference on Decision and Control","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Berkenkamp et al., 2017] Felix Berkenkamp, Matteo Turchetta, Angela Schoellig, and Andreas Krause. Safe model-based reinforcement learning with stability guaran- tees. Advances in neural information processing systems, 30, 2017.","title":"Safe model-based reinforcement learning with stability guarantees","authors":"Felix Berkenkamp, Matteo Turchetta, Angela Schoellig, Andreas Krause","year":"2017","venue":"Advances in neural information processing systems","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bharadhwaj et al., 2020] Homanga Bharadhwaj, Aviral Ku- mar, Nicholas Rhinehart, Sergey Levine, Florian Shkurti, and Animesh Garg. Conservative safety critics for explo- ration. arXiv preprint arXiv:2010.14497, 2020.","title":"Homanga Bharadhwaj, Aviral Kumar","authors":"Bharadhwaj","year":"2020","venue":"Conservative safety critics for exploration","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bohez et al., 2019] Steven Bohez, Abbas Abdolmaleki, Michael Neunert, Jonas Buchli, Nicolas Heess, and Raia Hadsell. Value constrained model-free continuous control. arXiv preprint arXiv:1902.04623, 2019.","title":"Value constrained model-free continuous control","authors":"Steven Bohez, Abbas Abdolmaleki, Michael Neunert, Jonas Buchli, Nicolas Heess, Raia Hadsell","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Brown and Sandholm, 2018] Noam Brown and Tuomas Sandholm. Superhuman ai for heads-up no-limit poker: Libratus beats top professionals. Science, 359(6374):418- 424, 2018.","title":"Noam Brown and Tuomas Sandholm. Superhuman ai for heads-up no-limit poker: Libratus beats top professionals","authors":"Sandholm Brown","year":"2018","venue":"Science","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Brunke et al., 2022] Lukas Brunke, Melissa Greeff, Adam W Hall, Zhaocong Yuan, Siqi Zhou, Jacopo Panerati, and Angela P Schoellig. Safe learning in robotics: From learning-based control to safe reinforce- ment learning. Annual Review of Control, Robotics, and Autonomous Systems, 5:411-444, 2022.","title":"Safe learning in robotics: From learning-based control to safe reinforcement learning","authors":"Lukas Brunke, Melissa Greeff, Adam W Hall, Zhaocong Yuan, Siqi Zhou, Jacopo Panerati, Angela P Schoellig","year":"2022","venue":"Annual Review of Control, Robotics, and Autonomous Systems","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Chen and Liu, 2021] Hongyi Chen and Changliu Liu. Safe and sample-efficient reinforcement learning for clustered dynamic environments. IEEE Control Systems Letters, 6:1928-1933, 2021.","title":"Safe and sample-efficient reinforcement learning for clustered dynamic environments","authors":"Chen, Liu ; ] Hongyi, Chen, Changliu Liu","year":"2021","venue":"IEEE Control Systems Letters","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Cheng et al., 2019] Richard Cheng, Gábor Orosz, Richard M Murray, and Joel W Burdick. End-to- end safe reinforcement learning through barrier functions for safety-critical continuous control tasks. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 3387-3395, 2019.","title":"End-toend safe reinforcement learning through barrier functions for safety-critical continuous control tasks","authors":"Richard Cheng, Gábor Orosz, Richard M Murray, Joel W Burdick","year":"2019","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Chow et al., 2018] Yinlam Chow, Ofir Nachum, Edgar Duenez-Guzman, and Mohammad Ghavamzadeh. A lyapunov-based approach to safe reinforcement learning. Advances in neural information processing systems, 31, 2018.","title":"A lyapunov-based approach to safe reinforcement learning","authors":"Chow","year":"2018","venue":"Advances in neural information processing systems","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Chow et al., 2019] Yinlam Chow, Ofir Nachum, Alek- sandra Faust, Edgar Duenez-Guzman, and Mohammad Ghavamzadeh. Lyapunov-based safe policy optimiza- tion for continuous control. ICML 2019 Workshop RL4RealLife, abs/1901.10031, 2019.","title":"Lyapunov-based safe policy optimization for continuous control","authors":"Chow","year":"2019","venue":"ICML 2019 Workshop RL4RealLife","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Chowdhury and Gopalan, 2017] Sayak Ray Chowdhury and Aditya Gopalan. On kernelized multi-armed bandits. In International Conference on Machine Learning, pages 844-853. PMLR, 2017.","title":"On kernelized multi-armed bandits","authors":"Gopalan ; Chowdhury, Ray Sayak, Aditya Chowdhury, Gopalan","year":"2017","venue":"International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Dalal et al., 2018] Gal Dalal, Krishnamurthy Dvijotham, Matej Vecerik, Todd Hester, Cosmin Paduraru, and Yu- val Tassa. Safe exploration in continuous action spaces. CoRR, abs/1801.08757, 2018.","title":"Safe exploration in continuous action spaces","authors":"Dalal","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Ferlez et al., 2020] James Ferlez, Mahmoud Elnaggar, Yasser Shoukry, and Cody Fleming. Shieldnn: A prov- ably safe nn filter for unsafe nn controllers. CoRR, abs/2006.09564, 2020.","title":"Shieldnn: A provably safe nn filter for unsafe nn controllers","authors":"James Ferlez, Mahmoud Elnaggar, Yasser Shoukry, Cody Fleming","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Fisac et al., 2018] Jaime F Fisac, Anayo K Akametalu, Melanie N Zeilinger, Shahab Kaynama, Jeremy Gillula, and Claire J Tomlin. A general safety framework for learning-based control in uncertain robotic systems. IEEE Transactions on Automatic Control, 64(7):2737-2752, 2018.","title":"A general safety framework for learning-based control in uncertain robotic systems","authors":"Jaime F Fisac, K Anayo, Melanie N Akametalu, Shahab Zeilinger, Jeremy Kaynama, Claire J Gillula, Tomlin","year":"2018","venue":"IEEE Transactions on Automatic Control","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Gu et al., 2022] Shangding Gu, Long Yang, Yali Du, Guang Chen, Florian Walter, Jun Wang, Yaodong Yang, and Alois Knoll. A review of safe reinforcement learning: Methods, theory and applications. arXiv preprint arXiv:2205.10330, 2022.","title":"A review of safe reinforcement learning: Methods, theory and applications","authors":"Gu","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[He et al., 2022] Tairan He, Yuge Zhang, Kan Ren, Minghuan Liu, Che Wang, Weinan Zhang, Yuqing Yang, and Dongsheng Li. Reinforcement learning with automated auxiliary loss search. arXiv preprint arXiv:2210.06041, 2022.","title":"Reinforcement learning with automated auxiliary loss search","authors":"Tairan He, Yuge Zhang, Kan Ren, Minghuan Liu, Che Wang, Weinan Zhang, Yuqing Yang, Dongsheng Li","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[He et al., 2023a] Suqin He, Weiye Zhao, Chuxiong Hu, Yu Zhu, and Changliu Liu. A hierarchical long short term safety framework for efficient robot manipulation under uncertainty. Robotics and Computer-Integrated Manufac- turing, 82:102522, 2023.","title":"A hierarchical long short term safety framework for efficient robot manipulation under uncertainty","authors":"He","year":"2023","venue":"Robotics and Computer-Integrated Manufacturing","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[He et al., 2023b] Tairan He, Weiye Zhao, and Changliu Liu. Autocost: Evolving intrinsic cost for zero-violation rein- forcement learning. Proceedings of the AAAI Conference on Artificial Intelligence, 2023.","title":"Autocost: Evolving intrinsic cost for zero-violation reinforcement learning","authors":"He","year":"2023","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Khalil and Grizzle, 2002] H.K. Khalil and J.W. Grizzle. Nonlinear Systems. Pearson Education. Prentice Hall, 2002.","title":"Nonlinear Systems","authors":"H K Khalil, J W Grizzle","year":"2002","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Kong et al., 2015] Jason Kong, Mark Pfeiffer, Georg Schildbach, and Francesco Borrelli. Kinematic and dy- namic vehicle models for autonomous driving control de- sign. In 2015 IEEE Intelligent Vehicles Symposium (IV), pages 1094-1099. IEEE, 2015.","title":"Kinematic and dynamic vehicle models for autonomous driving control design","authors":"Jason Kong, Mark Pfeiffer, Georg Schildbach, Francesco Borrelli","year":"2015","venue":"IEEE Intelligent Vehicles Symposium (IV)","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Liang et al., 2018] Qingkai Liang, Fanyu Que, and Ey- tan Modiano. Accelerated primal-dual policy optimiza- tion for safe reinforcement learning. arXiv preprint arXiv:1802.06480, 2018.","title":"Eytan Modiano. Accelerated primal-dual policy optimization for safe reinforcement learning","authors":"Liang","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Liu and Tomizuka, 2014] Changliu Liu and Masayoshi Tomizuka. Control in a safe set: Addressing safety in human-robot interactions. In ASME 2014 Dynamic Sys- tems and Control Conference. American Society of Me- chanical Engineers Digital Collection, 2014.","title":"Control in a safe set: Addressing safety in human-robot interactions","authors":"Tomizuka Liu, Changliu Liu, Masayoshi Tomizuka","year":"2014","venue":"ASME 2014 Dynamic Systems and Control Conference","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Liu et al., 2021] Yongshuai Liu, Avishai Halev, and Xin Liu. Policy learning with constraints in model-free rein- forcement learning: A survey. In The 30th International Joint Conference on Artificial Intelligence (IJCAI), 2021.","title":"Policy learning with constraints in model-free rein-forcement learning: A survey","authors":"Liu","year":"2021","venue":"The 30th International Joint Conference on Artificial Intelligence (IJCAI)","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Ma et al., 2021] Haitong Ma, Changliu Liu, Shengbo Eben Li, Sifa Zheng, Wenchao Sun, and Jianyu Chen. Learn zero-constraint-violation policy in model-free constrained reinforcement learning. arXiv preprint arXiv:2111.12953, 2021.","title":"Learn zero-constraint-violation policy in model-free constrained reinforcement learning","authors":"Haitong Ma, Changliu Liu, Eben Shengbo, Sifa Li, Wenchao Zheng, Jianyu Sun, Chen","year":"2021","venue":null,"doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Ma et al., 2022] Haitong Ma, Changliu Liu, Shengbo Eben Li, Sifa Zheng, and Jianyu Chen. Joint synthesis of safety certificate and safe control policy using constrained rein- forcement learning. In Learning for Dynamics and Control Conference, pages 97-109. PMLR, 2022.","title":"Joint synthesis of safety certificate and safe control policy using constrained reinforcement learning","authors":"Ma","year":"2022","venue":"Learning for Dynamics and Control Conference","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Noren et al., 2021] Charles Noren, Weiye Zhao, and Changliu Liu. Safe adaptation with multiplicative un- certainties using robust safe set algorithm. IFAC- PapersOnLine, 54(20):360-365, 2021.","title":"Safe adaptation with multiplicative uncertainties using robust safe set algorithm","authors":"Charles Noren, Weiye Zhao, Changliu Liu","year":"2021","venue":"IFAC-PapersOnLine","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Schulman et al., 2017] John Schulman, Filip Wolski, Pra- fulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. CoRR, abs/1707.06347, 2017.","title":"Proximal policy optimization algorithms","authors":"John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, Oleg Klimov","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Shao et al., 2021] Yifei Simon Shao, Chao Chen, Shreyas Kousik, and Ram Vasudevan. Reachability-based trajec- tory safeguard (rts): A safe and fast reinforcement learn- ing safety layer for continuous control. IEEE Robotics and Automation Letters, 6(2):3663-3670, 2021.","title":"Reachability-based trajectory safeguard (rts): A safe and fast reinforcement learning safety layer for continuous control","authors":"Simon Yifei, Chao Shao, Shreyas Chen, Ram Kousik, Vasudevan","year":"2021","venue":"IEEE Robotics and Automation Letters","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Strehl et al., 2006] Alexander L. Strehl, Lihong Li, Eric Wiewiora, John Langford, and Michael L. Littman. Pac model-free reinforcement learning. In Proceedings of the 23rd international conference on Machine learning, pages 881-888. ACM Press, 2006.","title":"Pac model-free reinforcement learning","authors":"Alexander L Strehl, Lihong Li, Eric Wiewiora, John Langford, Michael L Littman","year":"2006","venue":"Proceedings of the 23rd international conference on Machine learning","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Tessler et al., 2018] Chen Tessler, Daniel J Mankowitz, and Shie Mannor. arXiv preprint arXiv:1805.11074, 2018.","title":null,"authors":"Chen Tessler, Daniel J Mankowitz, Shie Mannor","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Thananjeyan et al., 2021] Brijen Thananjeyan, Ashwin Bal- akrishna, Suraj Nair, Michael Luo, Krishnan Srinivasan, Minho Hwang, Joseph E Gonzalez, Julian Ibarz, Chelsea Finn, and Ken Goldberg. Recovery rl: Safe reinforcement learning with learned recovery zones. IEEE Robotics and Automation Letters, 6(3):4915-4922, 2021.","title":"Recovery rl: Safe reinforcement learning with learned recovery zones","authors":"Thananjeyan","year":"2021","venue":"IEEE Robotics and Automation Letters","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Vinyals et al., 2019] Oriol Vinyals, Igor Babuschkin, Woj- ciech M Czarnecki, Michaël Mathieu, Andrew Dudzik, Junyoung Chung, David H Choi, Richard Powell, Timo Ewalds, Petko Georgiev, et al. Grandmaster level in star- craft ii using multi-agent reinforcement learning. Nature, 575(7782):350-354, 2019.","title":"Grandmaster level in starcraft ii using multi-agent reinforcement learning","authors":"Oriol Vinyals, Igor Babuschkin, Wojciech M Czarnecki, Michaël Mathieu, Andrew Dudzik, Junyoung Chung, David H Choi, Richard Powell, Timo Ewalds, Petko Georgiev","year":"2019","venue":"Nature","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Wachi and Sui, 2020] Akifumi Wachi and Yanan Sui. Safe reinforcement learning in constrained markov decision processes. In Proceedings of the 37th International Con- ference on Machine Learning, ICML'20. JMLR.org, 2020.","title":"Safe reinforcement learning in constrained markov decision processes","authors":"Sui Wachi, Akifumi Wachi, Yanan Sui","year":"2020","venue":"Proceedings of the 37th International Conference on Machine Learning, ICML'20","doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Wachi et al., 2018] Akifumi Wachi, Yanan Sui, Yisong Yue, and Masahiro Ono. Safe exploration and optimization of constrained mdps using gaussian processes. In Pro- ceedings of the AAAI Conference on Artificial Intelligence, 2018.","title":"Safe exploration and optimization of constrained mdps using gaussian processes","authors":"Akifumi Wachi, Yanan Sui, Yisong Yue, Masahiro Ono","year":"2018","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Wei and Liu, 2022] Tianhao Wei and Changliu Liu. Safe control with neural network dynamic models. In Learn- ing for Dynamics and Control Conference, pages 739-750.","title":"Safe control with neural network dynamic models","authors":"Liu ; ] Tianhao Wei, Changliu Wei, Liu","year":"2022","venue":"Learning for Dynamics and Control Conference","doi":null,"url":null,"internal_url":null},{"position":37,"raw":"PMLR, 2022.","title":null,"authors":"Pmlr","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":38,"raw":"[Wei et al., 2022] Tianhao Wei, Shucheng Kang, Weiye Zhao, and Changliu Liu. Persistently feasible robust safe control by safety index synthesis and convex semi-infinite programming. IEEE Control Systems Letters, 2022.","title":"Persistently feasible robust safe control by safety index synthesis and convex semi-infinite programming","authors":"Tianhao Wei, Shucheng Kang, Weiye Zhao, Changliu Liu","year":"2022","venue":"IEEE Control Systems Letters","doi":null,"url":null,"internal_url":null},{"position":39,"raw":"[Williams and Rasmussen, 2006] Christopher K Williams and Carl Edward Rasmussen. Gaussian processes for ma- chine learning. MIT press Cambridge, MA, 2006.","title":"Gaussian processes for machine learning","authors":"K Christopher, Carl Edward Williams, Rasmussen","year":"2006","venue":null,"doi":null,"url":null,"internal_url":null},{"position":40,"raw":"[Zhang et al., 2022] Linrui Zhang, Qin Zhang, Li Shen, Bo Yuan, Xueqian Wang, and Dacheng Tao. Evaluating model-free reinforcement learning toward safety-critical tasks. arXiv preprint arXiv:2212.05727, 2022.","title":"Evaluating model-free reinforcement learning toward safety-critical tasks","authors":"Zhang","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":41,"raw":"[Zhao et al., 2019a] W Zhao, Yang Liu, Xiaoming Zhao, J Qiu, and Jian Peng. Approximation gradient error vari- ance reduced optimization. In Workshop on Reinforcement Learning in Games (RLG) at The Thirty-Third AAAI Con- ference on Artificial Intelligence (AAAI-19), 2019.","title":"Approximation gradient error variance reduced optimization","authors":"Zhao","year":"2019","venue":"Workshop on Reinforcement Learning in Games (RLG) at The Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19)","doi":null,"url":null,"internal_url":null},{"position":42,"raw":"[Zhao et al., 2019b] Wei-Ye Zhao, Xi-Ya Guan, Yang Liu, Xiaoming Zhao, and Jian Peng. Stochastic variance reduc- tion for deep q-learning. arXiv preprint arXiv:1905.08152, 2019.","title":"Stochastic variance reduction for deep q-learning","authors":"Zhao","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":43,"raw":"[Zhao et al., 2020] Wei-Ye Zhao, Suqin He, Chengtao Wen, and Changliu Liu. Contact-rich trajectory generation in confined environments using iterative convex optimiza- tion. In Dynamic Systems and Control Conference, vol- ume 84287, page V002T31A002. American Society of Mechanical Engineers, 2020.","title":"Contact-rich trajectory generation in confined environments using iterative convex optimization","authors":"Wei-Ye Zhao, Suqin He, Chengtao Wen, Changliu Liu","year":"2020","venue":"Dynamic Systems and Control Conference","doi":null,"url":null,"internal_url":null},{"position":44,"raw":"[Zhao et al., 2021] Weiye Zhao, Tairan He, and Changliu Liu. Model-free safe control for zero-violation reinforce- ment learning. In 5th Annual Conference on Robot Learn- ing, 2021.","title":"Model-free safe control for zero-violation reinforcement learning","authors":"Weiye Zhao, Tairan He, Changliu Liu","year":"2021","venue":"5th Annual Conference on Robot Learning","doi":null,"url":null,"internal_url":null},{"position":45,"raw":"[Zhao et al., 2022a] Weiye Zhao, Suqin He, and Changliu Liu. Provably safe tolerance estimation for robot arms via sum-of-squares programming. IEEE Control Systems Let- ters, 6:3439-3444, 2022.","title":"Provably safe tolerance estimation for robot arms via sum-of-squares programming","authors":"Zhao","year":"2022","venue":"IEEE Control Systems Letters","doi":null,"url":null,"internal_url":null},{"position":46,"raw":"[Zhao et al., 2022b] Weiye Zhao, Tairan He, and Changliu Liu. Probabilistic safeguard for reinforcement learning us- ing safety index guided gaussian process models. arXiv preprint arXiv:2210.01041, 2022.","title":"Probabilistic safeguard for reinforcement learning using safety index guided gaussian process models","authors":"Zhao","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":47,"raw":"[Zhao et al., 2022c] Weiye Zhao, Tairan He, Tianhao Wei, Simin Liu, and Changliu Liu. Safety index synthe- sis via sum-of-squares programming. arXiv preprint arXiv:2209.09134, 2022.","title":"Safety index synthesis via sum-of-squares programming","authors":"Zhao","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}