[{"title":"Learning control policies for stochastic systems with reach-avoid guarantees","OA_place":"repository","publication":"arXiv","ec_funded":1,"date_published":"2022-11-29T00:00:00Z","type":"preprint","related_material":{"record":[{"id":"14830","relation":"later_version","status":"public"},{"id":"14539","relation":"dissertation_contains","status":"public"}]},"status":"public","article_processing_charge":"No","corr_author":"1","license":"https://creativecommons.org/licenses/by-sa/4.0/","date_created":"2023-11-24T13:10:09Z","oa":1,"day":"29","_id":"14600","abstract":[{"lang":"eng","text":"We study the problem of learning controllers for discrete-time non-linear stochastic dynamical systems with formal reach-avoid guarantees. This work presents the first method for providing formal reach-avoid guarantees, which combine and generalize stability and safety guarantees, with a tolerable probability threshold $p\\in[0,1]$ over the infinite time horizon. Our method leverages advances in machine learning literature and it represents formal certificates as neural networks. In particular, we learn a certificate in the form of a reach-avoid supermartingale (RASM), a novel notion that we introduce in this work. Our RASMs provide reachability and avoidance guarantees by imposing constraints on what can be viewed as a stochastic extension of level sets of Lyapunov functions for deterministic systems. Our approach solves several important problems -- it can be used to learn a control policy from scratch, to verify a reach-avoid specification for a fixed control policy, or to fine-tune a pre-trained policy if it does not satisfy the reach-avoid specification. We validate our approach on $3$ stochastic non-linear reinforcement learning tasks."}],"date_updated":"2026-04-07T13:27:56Z","language":[{"iso":"eng"}],"doi":"10.48550/ARXIV.2210.05308","citation":{"ista":"Zikelic D, Lechner M, Henzinger TA, Chatterjee K. Learning control policies for stochastic systems with reach-avoid guarantees. arXiv, 2210.05308.","ama":"Zikelic D, Lechner M, Henzinger TA, Chatterjee K. Learning control policies for stochastic systems with reach-avoid guarantees. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2210.05308\">10.48550/ARXIV.2210.05308</a>","apa":"Zikelic, D., Lechner, M., Henzinger, T. A., &#38; Chatterjee, K. (n.d.). Learning control policies for stochastic systems with reach-avoid guarantees. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2210.05308\">https://doi.org/10.48550/ARXIV.2210.05308</a>","chicago":"Zikelic, Dorde, Mathias Lechner, Thomas A Henzinger, and Krishnendu Chatterjee. “Learning Control Policies for Stochastic Systems with Reach-Avoid Guarantees.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2210.05308\">https://doi.org/10.48550/ARXIV.2210.05308</a>.","ieee":"D. Zikelic, M. Lechner, T. A. Henzinger, and K. Chatterjee, “Learning control policies for stochastic systems with reach-avoid guarantees,” <i>arXiv</i>. .","mla":"Zikelic, Dorde, et al. “Learning Control Policies for Stochastic Systems with Reach-Avoid Guarantees.” <i>ArXiv</i>, 2210.05308, doi:<a href=\"https://doi.org/10.48550/ARXIV.2210.05308\">10.48550/ARXIV.2210.05308</a>.","short":"D. Zikelic, M. Lechner, T.A. Henzinger, K. Chatterjee, ArXiv (n.d.)."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"11","year":"2022","tmp":{"short":"CC BY-SA (4.0)","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","image":"/images/cc_by_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode"},"article_number":"2210.05308","department":[{"_id":"KrCh"},{"_id":"ToHe"}],"oa_version":"Preprint","publication_status":"draft","project":[{"grant_number":"863818","call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications"},{"name":"Vigilant Algorithmic Monitoring of Software","_id":"62781420-2b32-11ec-9570-8d9b63373d4d","grant_number":"101020093","call_identifier":"H2020"},{"name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","call_identifier":"H2020"}],"external_id":{"arxiv":["2210.05308"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2210.05308"}],"author":[{"full_name":"Zikelic, Dorde","first_name":"Dorde","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4681-1699","last_name":"Zikelic"},{"full_name":"Lechner, Mathias","first_name":"Mathias","id":"3DC22916-F248-11E8-B48F-1D18A9856A87","last_name":"Lechner"},{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas A","full_name":"Henzinger, Thomas A","last_name":"Henzinger","orcid":"0000-0002-2985-7724"},{"orcid":"0000-0002-4561-241X","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"}],"arxiv":1}]