{"article_processing_charge":"No","_id":"18159","date_updated":"2024-10-07T07:49:10Z","title":"Certified policy verification and synthesis for MDPs under distributional reach-avoidance properties","external_id":{"arxiv":["2405.04015"]},"abstract":[{"lang":"eng","text":"Markov Decision Processes (MDPs) are a classical model for decision making in the presence of uncertainty. Often they are viewed as state transformers with planning objectives defned with respect to paths over MDP states. An increasingly\r\npopular alternative is to view them as distribution transformers, giving rise to a sequence of probability distributions over MDP states. For instance, reachability and safety properties in modeling robot swarms or chemical reaction networks are naturally defned in terms of probability distributions over states. Verifying such distributional properties is known to be hard and often beyond the reach of classical state-based verifcation techniques. In this work, we consider the problems of certifed policy (i.e. controller) verifcation and synthesis in MDPs under distributional reach-avoidance specifcations. By certifed we mean that, along with a policy, we also aim to synthesize a (checkable) certifcate ensuring that the MDP indeed satisfes the property. Thus, given the target set of distributions and an unsafe set of distributions over MDP states, our goal is to either synthesize a certifcate for a given policy or synthesize a policy along with a certifcate, proving that the target distribution can be reached while avoiding unsafe distributions. To solve this problem, we introduce the novel notion of distributional reach-avoid certifcates and present automated procedures for (1) synthesizing a certifcate for a given policy, and (2) synthesizing a policy together with the certifcate, both providing formal guarantees on certifcate correctness. Our experimental evaluation demonstrates the ability of our method to solve several non-trivial examples, including a multi-agent robot-swarm model, to synthesize certifed policies and to certify existing policies. "}],"language":[{"iso":"eng"}],"author":[{"first_name":"S","last_name":"Akshay","full_name":"Akshay, S"},{"first_name":"Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Meggendorfer, Tobias","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","first_name":"Tobias","last_name":"Meggendorfer","orcid":"0000-0002-1712-2165"},{"full_name":"Zikelic, Dorde","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","first_name":"Dorde","last_name":"Zikelic","orcid":"0000-0002-4681-1699"}],"date_published":"2024-09-01T00:00:00Z","status":"public","citation":{"mla":"Akshay, S., et al. “Certified Policy Verification and Synthesis for MDPs under Distributional Reach-Avoidance Properties.” <i>Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence</i>, International Joint Conferences on Artificial Intelligence, 2024, pp. 3–12.","apa":"Akshay, S., Chatterjee, K., Meggendorfer, T., &#38; Zikelic, D. (2024). Certified policy verification and synthesis for MDPs under distributional reach-avoidance properties. In <i>Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence</i> (pp. 3–12). Jeju, Korea: International Joint Conferences on Artificial Intelligence.","ieee":"S. Akshay, K. Chatterjee, T. Meggendorfer, and D. Zikelic, “Certified policy verification and synthesis for MDPs under distributional reach-avoidance properties,” in <i>Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence</i>, Jeju, Korea, 2024, pp. 3–12.","ista":"Akshay S, Chatterjee K, Meggendorfer T, Zikelic D. 2024. Certified policy verification and synthesis for MDPs under distributional reach-avoidance properties. Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence. IJCAI: International Joint Conference on Artificial Intelligence, 3–12.","chicago":"Akshay, S, Krishnendu Chatterjee, Tobias Meggendorfer, and Dorde Zikelic. “Certified Policy Verification and Synthesis for MDPs under Distributional Reach-Avoidance Properties.” In <i>Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence</i>, 3–12. International Joint Conferences on Artificial Intelligence, 2024.","short":"S. Akshay, K. Chatterjee, T. Meggendorfer, D. Zikelic, in:, Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence, International Joint Conferences on Artificial Intelligence, 2024, pp. 3–12.","ama":"Akshay S, Chatterjee K, Meggendorfer T, Zikelic D. Certified policy verification and synthesis for MDPs under distributional reach-avoidance properties. In: <i>Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence</i>. International Joint Conferences on Artificial Intelligence; 2024:3-12."},"publication_status":"published","month":"09","year":"2024","corr_author":"1","ec_funded":1,"scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2405.04015"}],"publication":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","publisher":"International Joint Conferences on Artificial Intelligence","day":"01","oa_version":"Preprint","department":[{"_id":"KrCh"}],"oa":1,"page":"3-12","conference":{"start_date":"2024-08-03","end_date":"2024-08-09","location":"Jeju, Korea","name":"IJCAI: International Joint Conference on Artificial Intelligence"},"publication_identifier":{"issn":["1045-0823"],"isbn":["9781956792041"]},"quality_controlled":"1","date_created":"2024-09-29T22:01:38Z","acknowledgement":"This work was supported in part by the ERC-2020-CoG 863818 (FoRM-SMArt), the Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 1 grant, Google Research Award 2023 and the SBI Foundation Hub for Data and Analytics.","project":[{"_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818"}],"type":"conference"}