{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T05:46:56Z","timestamp":1776750416192,"version":"3.51.2"},"reference-count":45,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"6","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62573021"],"award-info":[{"award-number":["62573021"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key Research and Development Program of China","award":["2025YFE0216900"],"award-info":[{"award-number":["2025YFE0216900"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Robot. Autom. Lett."],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1109\/lra.2026.3681154","type":"journal-article","created":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T19:58:34Z","timestamp":1775505514000},"page":"6823-6830","source":"Crossref","is-referenced-by-count":0,"title":["Safe Policy Optimization With Cost Practical Stability: A DQ-Learning Method"],"prefix":"10.1109","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-7182-2164","authenticated-orcid":false,"given":"Chenyu","family":"Wang","sequence":"first","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-1988-7008","authenticated-orcid":false,"given":"Linkai","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8216-8998","authenticated-orcid":false,"given":"Quan","family":"Quan","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref1","volume-title":"Reinforcement Learning: An Introduction","author":"Sutton","year":"2018"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-97-3944-8"},{"issue":"285","key":"ref3","first-page":"1","article-title":"OmniSafe: An infrastructure for accelerating safe reinforcement learning research","volume":"25","author":"Ji","year":"2024","journal-title":"J. Mach. Learn. Res."},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1201\/9781315140223"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2018.8619572"},{"key":"ref6","first-page":"25636","article-title":"Reachability constrained reinforcement learning","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Yu","year":"2022"},{"key":"ref7","article-title":"Constrained model-based reinforcement learning with robust cross-entropy method","author":"Liu","year":"2020"},{"key":"ref8","article-title":"Constrained policy optimization via Bayesian world models","volume-title":"Proc. Int. Conf. Learn. Representations","author":"As","year":"2022"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA48506.2021.9561593"},{"key":"ref10","first-page":"8103","article-title":"A Lyapunov-Based Approach to Safe Reinforcement Learning","volume-title":"Proc. Adv. Neural Info. Proces. Syst.","volume":"31","author":"Chow","year":"2018"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2024.120261"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2020.3011351"},{"key":"ref13","first-page":"1154","article-title":"A policy optimization method towards optimal-time stability","volume-title":"Conf. Robot Learn.","author":"Wang","year":"2023"},{"key":"ref14","first-page":"1384","article-title":"Control with patterns: A D-learning method","volume-title":"Proc. Conf. Robot Learn.","author":"Quan","year":"2024"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/9.871771"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/BF00992698"},{"key":"ref17","article-title":"Maximum a posteriori policy optimisation","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Abdolmaleki","year":"2018"},{"key":"ref18","first-page":"13644","article-title":"Constrained variational policy optimization for safe reinforcement learning","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Liu","year":"2022"},{"issue":"1","key":"ref19","first-page":"1437","article-title":"A comprehensive survey on safe reinforcement learning","volume":"16","author":"Garc","year":"2015","journal-title":"J. Mach. Learn. Res."},{"key":"ref20","first-page":"1889","article-title":"Trust region policy optimization","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Schulman","year":"2015"},{"key":"ref21","first-page":"22","article-title":"Constrained policy optimization","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Achiam","year":"2017"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2024\/913"},{"key":"ref23","article-title":"A survey of safe reinforcement learning and constrained MDPS: A technical survey on single-agent and multi-agent safety","author":"Kushwaha","year":"2025"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2021.3070252"},{"key":"ref25","article-title":"State-wise constrained policy optimization","author":"Zhao","year":"2024","journal-title":"Trans. Mach. Learn. Res"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1080\/00207179208934253"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2022.3232542"},{"key":"ref28","article-title":"Reinforcement learning and control as probabilistic inference: Tutorial and review","author":"Levine","year":"2018"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/OJCSYS.2024.3449138"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2019.8794107"},{"key":"ref31","article-title":"CBF-RL: Safety filtering reinforcement learning in training with control barrier functions","author":"Yang","year":"2025"},{"key":"ref32","volume-title":"Markov Decision Processes: Discrete Stochastic Dynamic Programming","author":"Puterman","year":"2014"},{"key":"ref33","article-title":"Benchmarking safe exploration in deep reinforcement learning","author":"Ray","year":"2019"},{"key":"ref34","first-page":"9133","article-title":"Responsive safety in reinforcement learning by PiD Lagrangian methods","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Stooke","year":"2020"},{"key":"ref35","article-title":"Bullet-safety-gym: A framework for constrained reinforcement learning","author":"Gronauer","year":"2022"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.52202\/075280-0831"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2023.3286102"},{"key":"ref38","article-title":"Continuous control with deep reinforcement learning","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Lillicrap","year":"2016"},{"key":"ref39","article-title":"Proximal policy optimization algorithms","author":"Schulman","year":"2017"},{"key":"ref40","first-page":"1861","article-title":"Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Haarnoja","year":"2018"},{"key":"ref41","first-page":"1587","article-title":"Addressing function approximation error in actor-critic methods","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Fujimoto","year":"2018"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.52202\/075280-3058"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v33i01.33013387"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1016\/j.ast.2021.106727"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1002\/cjs.11166"}],"container-title":["IEEE Robotics and Automation Letters"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/7083369\/11481819\/11474874.pdf?arnumber=11474874","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T05:19:09Z","timestamp":1776748749000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/11474874\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":45,"journal-issue":{"issue":"6"},"URL":"https:\/\/doi.org\/10.1109\/lra.2026.3681154","relation":{},"ISSN":["2377-3766","2377-3774"],"issn-type":[{"value":"2377-3766","type":"electronic"},{"value":"2377-3774","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6]]}}}