[{"file":[{"success":1,"file_size":867363,"relation":"main_file","content_type":"application/pdf","date_created":"2024-02-26T09:04:58Z","date_updated":"2024-02-26T09:04:58Z","file_name":"2024_LIPICs_Hirvonen.pdf","access_level":"open_access","file_id":"15028","checksum":"4fc7eea6e4ba140b904781fc7df868ec","creator":"dernst"}],"author":[{"full_name":"Hirvonen, Juho","last_name":"Hirvonen","first_name":"Juho"},{"full_name":"Schmid, Laura","last_name":"Schmid","id":"38B437DE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6978-7329","first_name":"Laura"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"first_name":"Stefan","last_name":"Schmid","full_name":"Schmid, Stefan"}],"project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"18","acknowledgement":"This work was partially funded by the Academy of Finland, grant 314888, the European Research Council CoG 863818 (ForM-SMArt), and the Austrian Science Fund (FWF) project I 4800-N (ADVISE). LS was supported by the Stochastic Analysis and Application Research Center (SAARC) under National Research Foundation of Korea grant NRF-2019R1A5A1028324.","alternative_title":["LIPIcs"],"title":"On the convergence time in graphical games: A locality-sensitive approach","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"KrCh"}],"language":[{"iso":"eng"}],"type":"conference","publication":"27th International Conference on Principles of Distributed Systems","date_created":"2024-02-18T23:01:01Z","has_accepted_license":"1","volume":286,"quality_controlled":"1","external_id":{"arxiv":["2102.13457"]},"article_processing_charge":"No","_id":"15006","article_number":"11","year":"2024","arxiv":1,"abstract":[{"text":"Graphical games are a useful framework for modeling the interactions of (selfish) agents who are connected via an underlying topology and whose behaviors influence each other. They have wide applications ranging from computer science to economics and biology. Yet, even though an agent’s payoff only depends on the actions of their direct neighbors in graphical games, computing the Nash equilibria and making statements about the convergence time of \"natural\" local dynamics in particular can be highly challenging. In this work, we present a novel approach for classifying complexity of Nash equilibria in graphical games by establishing a connection to local graph algorithms, a subfield of distributed computing. In particular, we make the observation that the equilibria of graphical games are equivalent to locally verifiable labelings (LVL) in graphs; vertex labelings which are verifiable with constant-round local algorithms. This connection allows us to derive novel lower bounds on the convergence time to equilibrium of best-response dynamics in graphical games. Since we establish that distributed convergence can sometimes be provably slow, we also introduce and give bounds on an intuitive notion of \"time-constrained\" inefficiency of best responses. We exemplify how our results can be used in the implementation of mechanisms that ensure convergence of best responses to a Nash equilibrium. Our results thus also give insight into the convergence of strategy-proof algorithms for graphical games, which is still not well understood.","lang":"eng"}],"date_updated":"2025-07-14T09:10:03Z","ec_funded":1,"month":"01","oa":1,"publication_identifier":{"issn":["18688969"],"isbn":["9783959773089"]},"status":"public","date_published":"2024-01-18T00:00:00Z","oa_version":"Published Version","doi":"10.4230/LIPIcs.OPODIS.2023.11","publication_status":"published","conference":{"end_date":"2023-12-08","location":"Tokyo, Japan","start_date":"2023-12-06","name":"OPODIS: Conference on Principles of Distributed Systems"},"intvolume":"       286","citation":{"mla":"Hirvonen, Juho, et al. “On the Convergence Time in Graphical Games: A Locality-Sensitive Approach.” <i>27th International Conference on Principles of Distributed Systems</i>, vol. 286, 11, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2023.11\">10.4230/LIPIcs.OPODIS.2023.11</a>.","ista":"Hirvonen J, Schmid L, Chatterjee K, Schmid S. 2024. On the convergence time in graphical games: A locality-sensitive approach. 27th International Conference on Principles of Distributed Systems. OPODIS: Conference on Principles of Distributed Systems, LIPIcs, vol. 286, 11.","apa":"Hirvonen, J., Schmid, L., Chatterjee, K., &#38; Schmid, S. (2024). On the convergence time in graphical games: A locality-sensitive approach. In <i>27th International Conference on Principles of Distributed Systems</i> (Vol. 286). Tokyo, Japan: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2023.11\">https://doi.org/10.4230/LIPIcs.OPODIS.2023.11</a>","chicago":"Hirvonen, Juho, Laura Schmid, Krishnendu Chatterjee, and Stefan Schmid. “On the Convergence Time in Graphical Games: A Locality-Sensitive Approach.” In <i>27th International Conference on Principles of Distributed Systems</i>, Vol. 286. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2023.11\">https://doi.org/10.4230/LIPIcs.OPODIS.2023.11</a>.","short":"J. Hirvonen, L. Schmid, K. Chatterjee, S. Schmid, in:, 27th International Conference on Principles of Distributed Systems, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","ieee":"J. Hirvonen, L. Schmid, K. Chatterjee, and S. Schmid, “On the convergence time in graphical games: A locality-sensitive approach,” in <i>27th International Conference on Principles of Distributed Systems</i>, Tokyo, Japan, 2024, vol. 286.","ama":"Hirvonen J, Schmid L, Chatterjee K, Schmid S. On the convergence time in graphical games: A locality-sensitive approach. In: <i>27th International Conference on Principles of Distributed Systems</i>. Vol 286. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.OPODIS.2023.11\">10.4230/LIPIcs.OPODIS.2023.11</a>"},"ddc":["000"],"scopus_import":"1","file_date_updated":"2024-02-26T09:04:58Z"},{"quality_controlled":"1","volume":13966,"article_processing_charge":"Yes (in subscription journal)","language":[{"iso":"eng"}],"department":[{"_id":"KrCh"}],"type":"conference","page":"86-112","date_created":"2023-09-10T22:01:12Z","publication":"International Conference on Computer Aided Verification","has_accepted_license":"1","alternative_title":["LNCS"],"title":"MDPs as distribution transformers: Affine invariant synthesis for safety objectives","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"relation":"main_file","content_type":"application/pdf","success":1,"file_size":531745,"file_name":"2023_LNCS_Akshay.pdf","date_updated":"2023-09-20T08:46:43Z","date_created":"2023-09-20T08:46:43Z","file_id":"14349","checksum":"f143c8eedf609f20f2aad2eeb496d53f","creator":"dernst","access_level":"open_access"}],"project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"},{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"}],"author":[{"full_name":"Akshay, S.","last_name":"Akshay","first_name":"S."},{"full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","orcid":"0000-0002-4561-241X"},{"orcid":"0000-0002-1712-2165","first_name":"Tobias","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","last_name":"Meggendorfer","full_name":"Meggendorfer, Tobias"},{"orcid":"0000-0002-4681-1699","first_name":"Dorde","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","last_name":"Zikelic","full_name":"Zikelic, Dorde"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"17","acknowledgement":"This work was supported in part by the ERC CoG 863818 (FoRM-SMArt) and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 as well as DST/CEFIPRA/INRIA project EQuaVE and SERB Matrices grant MTR/2018/00074.","intvolume":"     13966","citation":{"mla":"Akshay, S., et al. “MDPs as Distribution Transformers: Affine Invariant Synthesis for Safety Objectives.” <i>International Conference on Computer Aided Verification</i>, vol. 13966, Springer Nature, 2023, pp. 86–112, doi:<a href=\"https://doi.org/10.1007/978-3-031-37709-9_5\">10.1007/978-3-031-37709-9_5</a>.","ista":"Akshay S, Chatterjee K, Meggendorfer T, Zikelic D. 2023. MDPs as distribution transformers: Affine invariant synthesis for safety objectives. International Conference on Computer Aided Verification. CAV: Computer Aided Verification, LNCS, vol. 13966, 86–112.","apa":"Akshay, S., Chatterjee, K., Meggendorfer, T., &#38; Zikelic, D. (2023). MDPs as distribution transformers: Affine invariant synthesis for safety objectives. In <i>International Conference on Computer Aided Verification</i> (Vol. 13966, pp. 86–112). Paris, France: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-37709-9_5\">https://doi.org/10.1007/978-3-031-37709-9_5</a>","chicago":"Akshay, S., Krishnendu Chatterjee, Tobias Meggendorfer, and Dorde Zikelic. “MDPs as Distribution Transformers: Affine Invariant Synthesis for Safety Objectives.” In <i>International Conference on Computer Aided Verification</i>, 13966:86–112. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/978-3-031-37709-9_5\">https://doi.org/10.1007/978-3-031-37709-9_5</a>.","short":"S. Akshay, K. Chatterjee, T. Meggendorfer, D. Zikelic, in:, International Conference on Computer Aided Verification, Springer Nature, 2023, pp. 86–112.","ama":"Akshay S, Chatterjee K, Meggendorfer T, Zikelic D. MDPs as distribution transformers: Affine invariant synthesis for safety objectives. In: <i>International Conference on Computer Aided Verification</i>. Vol 13966. Springer Nature; 2023:86-112. doi:<a href=\"https://doi.org/10.1007/978-3-031-37709-9_5\">10.1007/978-3-031-37709-9_5</a>","ieee":"S. Akshay, K. Chatterjee, T. Meggendorfer, and D. Zikelic, “MDPs as distribution transformers: Affine invariant synthesis for safety objectives,” in <i>International Conference on Computer Aided Verification</i>, Paris, France, 2023, vol. 13966, pp. 86–112."},"ddc":["000"],"scopus_import":"1","file_date_updated":"2023-09-20T08:46:43Z","date_published":"2023-07-17T00:00:00Z","oa_version":"Published Version","publication_status":"published","conference":{"end_date":"2023-07-22","location":"Paris, France","start_date":"2023-07-17","name":"CAV: Computer Aided Verification"},"doi":"10.1007/978-3-031-37709-9_5","ec_funded":1,"month":"07","publication_identifier":{"issn":["0302-9743"],"isbn":["9783031377082"],"eissn":["1611-3349"]},"oa":1,"status":"public","_id":"14317","year":"2023","date_updated":"2025-07-14T09:09:56Z","abstract":[{"text":"Markov decision processes can be viewed as transformers of probability distributions. While this view is useful from a practical standpoint to reason about trajectories of distributions, basic reachability and safety problems are known to be computationally intractable (i.e., Skolem-hard) to solve in such models. Further, we show that even for simple examples of MDPs, strategies for safety objectives over distributions can require infinite memory and randomization.\r\nIn light of this, we present a novel overapproximation approach to synthesize strategies in an MDP, such that a safety objective over the distributions is met. More precisely, we develop a new framework for template-based synthesis of certificates as affine distributional and inductive invariants for safety objectives in MDPs. We provide two algorithms within this framework. One can only synthesize memoryless strategies, but has relative completeness guarantees, while the other can synthesize general strategies. The runtime complexity of both algorithms is in PSPACE. We implement these algorithms and show that they can solve several non-trivial examples.","lang":"eng"}]},{"ddc":["000"],"scopus_import":"1","file_date_updated":"2023-09-20T08:24:47Z","citation":{"short":"Y. Sun, H. Fu, K. Chatterjee, A.K. Goharshady, in:, Computer Aided Verification, Springer Nature, 2023, pp. 16–39.","ieee":"Y. Sun, H. Fu, K. Chatterjee, and A. K. Goharshady, “Automated tail bound analysis for probabilistic recurrence relations,” in <i>Computer Aided Verification</i>, Paris, France, 2023, vol. 13966, pp. 16–39.","ama":"Sun Y, Fu H, Chatterjee K, Goharshady AK. Automated tail bound analysis for probabilistic recurrence relations. In: <i>Computer Aided Verification</i>. Vol 13966. Springer Nature; 2023:16-39. doi:<a href=\"https://doi.org/10.1007/978-3-031-37709-9_2\">10.1007/978-3-031-37709-9_2</a>","chicago":"Sun, Yican, Hongfei Fu, Krishnendu Chatterjee, and Amir Kafshdar Goharshady. “Automated Tail Bound Analysis for Probabilistic Recurrence Relations.” In <i>Computer Aided Verification</i>, 13966:16–39. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/978-3-031-37709-9_2\">https://doi.org/10.1007/978-3-031-37709-9_2</a>.","mla":"Sun, Yican, et al. “Automated Tail Bound Analysis for Probabilistic Recurrence Relations.” <i>Computer Aided Verification</i>, vol. 13966, Springer Nature, 2023, pp. 16–39, doi:<a href=\"https://doi.org/10.1007/978-3-031-37709-9_2\">10.1007/978-3-031-37709-9_2</a>.","apa":"Sun, Y., Fu, H., Chatterjee, K., &#38; Goharshady, A. K. (2023). Automated tail bound analysis for probabilistic recurrence relations. In <i>Computer Aided Verification</i> (Vol. 13966, pp. 16–39). Paris, France: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-37709-9_2\">https://doi.org/10.1007/978-3-031-37709-9_2</a>","ista":"Sun Y, Fu H, Chatterjee K, Goharshady AK. 2023. Automated tail bound analysis for probabilistic recurrence relations. Computer Aided Verification. CAV: Computer Aided Verification, LNCS, vol. 13966, 16–39."},"intvolume":"     13966","publication_status":"published","conference":{"end_date":"2023-07-22","location":"Paris, France","start_date":"2023-07-17","name":"CAV: Computer Aided Verification"},"doi":"10.1007/978-3-031-37709-9_2","date_published":"2023-07-17T00:00:00Z","oa_version":"Published Version","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783031377082"]},"oa":1,"status":"public","ec_funded":1,"month":"07","year":"2023","date_updated":"2025-07-14T09:09:57Z","abstract":[{"text":"Probabilistic recurrence relations (PRRs) are a standard formalism for describing the runtime of a randomized algorithm. Given a PRR and a time limit κ, we consider the tail probability Pr[T≥κ], i.e., the probability that the randomized runtime T of the PRR exceeds κ. Our focus is the formal analysis of tail bounds that aims at finding a tight asymptotic upper bound u≥Pr[T≥κ]. To address this problem, the classical and most well-known approach is the cookbook method by Karp (JACM 1994), while other approaches are mostly limited to deriving tail bounds of specific PRRs via involved custom analysis.\r\nIn this work, we propose a novel approach for deriving the common exponentially-decreasing tail bounds for PRRs whose preprocessing time and random passed sizes observe discrete or (piecewise) uniform distribution and whose recursive call is either a single procedure call or a divide-and-conquer. We first establish a theoretical approach via Markov’s inequality, and then instantiate the theoretical approach with a template-based algorithmic approach via a refined treatment of exponentiation. Experimental evaluation shows that our algorithmic approach is capable of deriving tail bounds that are (i) asymptotically tighter than Karp’s method, (ii) match the best-known manually-derived asymptotic tail bound for QuickSelect, and (iii) is only slightly worse (with a loglogn factor) than the manually-proven optimal asymptotic tail bound for QuickSort. Moreover, our algorithmic approach handles all examples (including realistic PRRs such as QuickSort, QuickSelect, DiameterComputation, etc.) in less than 0.1 s, showing that our approach is efficient in practice.","lang":"eng"}],"_id":"14318","article_processing_charge":"Yes (in subscription journal)","related_material":{"link":[{"relation":"software","url":"https://github.com/boyvolcano/PRR"}]},"volume":13966,"quality_controlled":"1","date_created":"2023-09-10T22:01:12Z","page":"16-39","publication":"Computer Aided Verification","has_accepted_license":"1","language":[{"iso":"eng"}],"department":[{"_id":"KrCh"}],"type":"conference","title":"Automated tail bound analysis for probabilistic recurrence relations","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","alternative_title":["LNCS"],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"17","acknowledgement":"We thank Prof. Bican Xia for valuable information on the exponential theory of reals. The work is partially supported by the National Natural Science Foundation of China (NSFC) with Grant No. 62172271, ERC CoG 863818 (ForM-SMArt), the Hong Kong Research Grants Council ECS Project Number 26208122, the HKUST-Kaisa Joint Research Institute Project Grant HKJRI3A-055 and the HKUST Startup Grant R9272.","file":[{"creator":"dernst","file_id":"14348","checksum":"42917e086f8c7699f3bccf84f74fe000","access_level":"open_access","file_name":"2023_LNCS_Sun.pdf","date_updated":"2023-09-20T08:24:47Z","date_created":"2023-09-20T08:24:47Z","content_type":"application/pdf","relation":"main_file","file_size":624647,"success":1}],"project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"}],"author":[{"full_name":"Sun, Yican","first_name":"Yican","last_name":"Sun"},{"full_name":"Fu, Hongfei","first_name":"Hongfei","last_name":"Fu"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"first_name":"Amir Kafshdar","orcid":"0000-0003-1702-6584","id":"391365CE-F248-11E8-B48F-1D18A9856A87","last_name":"Goharshady","full_name":"Goharshady, Amir Kafshdar"}]},{"oa":1,"publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959772921"]},"status":"public","ec_funded":1,"month":"08","year":"2023","date_updated":"2025-07-14T09:09:57Z","arxiv":1,"abstract":[{"lang":"eng","text":"Entropic risk (ERisk) is an established risk measure in finance, quantifying risk by an exponential re-weighting of rewards. We study ERisk for the first time in the context of turn-based stochastic games with the total reward objective. This gives rise to an objective function that demands the control of systems in a risk-averse manner. We show that the resulting games are determined and, in particular, admit optimal memoryless deterministic strategies. This contrasts risk measures that previously have been considered in the special case of Markov decision processes and that require randomization and/or memory. We provide several results on the decidability and the computational complexity of the threshold problem, i.e. whether the optimal value of ERisk exceeds a given threshold. In the most general case, the problem is decidable subject to Shanuel’s conjecture. If all inputs are rational, the resulting threshold problem can be solved using algebraic numbers, leading to decidability via a polynomial-time reduction to the existential theory of the reals. Further restrictions on the encoding of the input allow the solution of the threshold problem in NP∩coNP. Finally, an approximation algorithm for the optimal value of ERisk is provided."}],"_id":"14417","article_number":"15","ddc":["000"],"scopus_import":"1","file_date_updated":"2023-10-09T09:19:11Z","citation":{"chicago":"Baier, Christel, Krishnendu Chatterjee, Tobias Meggendorfer, and Jakob Piribauer. “Entropic Risk for Turn-Based Stochastic Games.” In <i>48th International Symposium on Mathematical Foundations of Computer Science</i>, Vol. 272. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2023.15\">https://doi.org/10.4230/LIPIcs.MFCS.2023.15</a>.","apa":"Baier, C., Chatterjee, K., Meggendorfer, T., &#38; Piribauer, J. (2023). Entropic risk for turn-based stochastic games. In <i>48th International Symposium on Mathematical Foundations of Computer Science</i> (Vol. 272). Bordeaux, France: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2023.15\">https://doi.org/10.4230/LIPIcs.MFCS.2023.15</a>","ista":"Baier C, Chatterjee K, Meggendorfer T, Piribauer J. 2023. Entropic risk for turn-based stochastic games. 48th International Symposium on Mathematical Foundations of Computer Science. MFCS: Symposium on Mathematical Foundations of Computer Science, LIPIcs, vol. 272, 15.","mla":"Baier, Christel, et al. “Entropic Risk for Turn-Based Stochastic Games.” <i>48th International Symposium on Mathematical Foundations of Computer Science</i>, vol. 272, 15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2023.15\">10.4230/LIPIcs.MFCS.2023.15</a>.","short":"C. Baier, K. Chatterjee, T. Meggendorfer, J. Piribauer, in:, 48th International Symposium on Mathematical Foundations of Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.","ama":"Baier C, Chatterjee K, Meggendorfer T, Piribauer J. Entropic risk for turn-based stochastic games. In: <i>48th International Symposium on Mathematical Foundations of Computer Science</i>. Vol 272. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2023.15\">10.4230/LIPIcs.MFCS.2023.15</a>","ieee":"C. Baier, K. Chatterjee, T. Meggendorfer, and J. Piribauer, “Entropic risk for turn-based stochastic games,” in <i>48th International Symposium on Mathematical Foundations of Computer Science</i>, Bordeaux, France, 2023, vol. 272."},"intvolume":"       272","publication_status":"published","conference":{"end_date":"2023-09-01","location":"Bordeaux, France","start_date":"2023-08-28","name":"MFCS: Symposium on Mathematical Foundations of Computer Science"},"doi":"10.4230/LIPIcs.MFCS.2023.15","date_published":"2023-08-21T00:00:00Z","oa_version":"Published Version","title":"Entropic risk for turn-based stochastic games","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","alternative_title":["LIPIcs"],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"21","acknowledgement":"This work was partly funded by the ERC CoG 863818 (ForM-SMArt), the DFG Grant\r\n389792660 as part of TRR 248 (Foundations of Perspicuous Software Systems), the Cluster of\r\nExcellence EXC 2050/1 (CeTI, project ID 390696704, as part of Germany’s Excellence Strategy), and the DFG projects BA-1679/11-1 and BA-1679/12-1.","file":[{"date_created":"2023-10-09T09:19:11Z","file_name":"2023_LIPIcsMFCS_Baier.pdf","date_updated":"2023-10-09T09:19:11Z","access_level":"open_access","checksum":"402281b17ed669bbf149d0fdf68ac201","file_id":"14418","creator":"dernst","success":1,"file_size":826843,"relation":"main_file","content_type":"application/pdf"}],"project":[{"_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications"}],"author":[{"full_name":"Baier, Christel","last_name":"Baier","first_name":"Christel"},{"first_name":"Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu"},{"full_name":"Meggendorfer, Tobias","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","last_name":"Meggendorfer","first_name":"Tobias","orcid":"0000-0002-1712-2165"},{"last_name":"Piribauer","first_name":"Jakob","full_name":"Piribauer, Jakob"}],"article_processing_charge":"Yes","external_id":{"arxiv":["2307.06611"]},"quality_controlled":"1","volume":272,"date_created":"2023-10-09T09:21:05Z","publication":"48th International Symposium on Mathematical Foundations of Computer Science","has_accepted_license":"1","language":[{"iso":"eng"}],"department":[{"_id":"KrCh"}],"type":"conference"},{"doi":"10.1007/978-3-031-45329-8_17","publication_status":"published","conference":{"start_date":"2023-10-24","name":"ATVA: Automated Technology for Verification and Analysis","end_date":"2023-10-27","location":"Singapore, Singapore"},"oa_version":"None","date_published":"2023-10-22T00:00:00Z","scopus_import":"1","citation":{"chicago":"Ansaripour, Matin, Krishnendu Chatterjee, Thomas A Henzinger, Mathias Lechner, and Dorde Zikelic. “Learning Provably Stabilizing Neural Controllers for Discrete-Time Stochastic Systems.” In <i>21st International Symposium on Automated Technology for Verification and Analysis</i>, 14215:357–79. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/978-3-031-45329-8_17\">https://doi.org/10.1007/978-3-031-45329-8_17</a>.","mla":"Ansaripour, Matin, et al. “Learning Provably Stabilizing Neural Controllers for Discrete-Time Stochastic Systems.” <i>21st International Symposium on Automated Technology for Verification and Analysis</i>, vol. 14215, Springer Nature, 2023, pp. 357–79, doi:<a href=\"https://doi.org/10.1007/978-3-031-45329-8_17\">10.1007/978-3-031-45329-8_17</a>.","apa":"Ansaripour, M., Chatterjee, K., Henzinger, T. A., Lechner, M., &#38; Zikelic, D. (2023). Learning provably stabilizing neural controllers for discrete-time stochastic systems. In <i>21st International Symposium on Automated Technology for Verification and Analysis</i> (Vol. 14215, pp. 357–379). Singapore, Singapore: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-45329-8_17\">https://doi.org/10.1007/978-3-031-45329-8_17</a>","ista":"Ansaripour M, Chatterjee K, Henzinger TA, Lechner M, Zikelic D. 2023. Learning provably stabilizing neural controllers for discrete-time stochastic systems. 21st International Symposium on Automated Technology for Verification and Analysis. ATVA: Automated Technology for Verification and Analysis, LNCS, vol. 14215, 357–379.","short":"M. Ansaripour, K. Chatterjee, T.A. Henzinger, M. Lechner, D. Zikelic, in:, 21st International Symposium on Automated Technology for Verification and Analysis, Springer Nature, 2023, pp. 357–379.","ieee":"M. Ansaripour, K. Chatterjee, T. A. Henzinger, M. Lechner, and D. Zikelic, “Learning provably stabilizing neural controllers for discrete-time stochastic systems,” in <i>21st International Symposium on Automated Technology for Verification and Analysis</i>, Singapore, Singapore, 2023, vol. 14215, pp. 357–379.","ama":"Ansaripour M, Chatterjee K, Henzinger TA, Lechner M, Zikelic D. Learning provably stabilizing neural controllers for discrete-time stochastic systems. In: <i>21st International Symposium on Automated Technology for Verification and Analysis</i>. Vol 14215. Springer Nature; 2023:357-379. doi:<a href=\"https://doi.org/10.1007/978-3-031-45329-8_17\">10.1007/978-3-031-45329-8_17</a>"},"intvolume":"     14215","abstract":[{"text":"We consider the problem of learning control policies in discrete-time stochastic systems which guarantee that the system stabilizes within some specified stabilization region with probability 1. Our approach is based on the novel notion of stabilizing ranking supermartingales (sRSMs) that we introduce in this work. Our sRSMs overcome the limitation of methods proposed in previous works whose applicability is restricted to systems in which the stabilizing region cannot be left once entered under any control policy. We present a learning procedure that learns a control policy together with an sRSM that formally certifies probability 1 stability, both learned as neural networks. We show that this procedure can also be adapted to formally verifying that, under a given Lipschitz continuous control policy, the stochastic system stabilizes within some stabilizing region with probability 1. Our experimental evaluation shows that our learning procedure can successfully learn provably stabilizing policies in practice.","lang":"eng"}],"date_updated":"2025-07-14T09:09:59Z","year":"2023","_id":"14559","status":"public","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783031453281"],"issn":["0302-9743"]},"month":"10","ec_funded":1,"publication":"21st International Symposium on Automated Technology for Verification and Analysis","page":"357-379","date_created":"2023-11-19T23:00:56Z","type":"conference","department":[{"_id":"ToHe"},{"_id":"KrCh"}],"language":[{"iso":"eng"}],"article_processing_charge":"No","volume":14215,"quality_controlled":"1","acknowledgement":"This work was supported in part by the ERC-2020-AdG 101020093, ERC CoG 863818 (FoRM-SMArt) and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385.","day":"22","author":[{"full_name":"Ansaripour, Matin","last_name":"Ansaripour","first_name":"Matin"},{"full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","first_name":"Krishnendu"},{"full_name":"Henzinger, Thomas A","orcid":"0000-0002-2985-7724","first_name":"Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger"},{"full_name":"Lechner, Mathias","last_name":"Lechner","id":"3DC22916-F248-11E8-B48F-1D18A9856A87","first_name":"Mathias"},{"last_name":"Zikelic","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4681-1699","first_name":"Dorde","full_name":"Zikelic, Dorde"}],"project":[{"grant_number":"101020093","_id":"62781420-2b32-11ec-9570-8d9b63373d4d","call_identifier":"H2020","name":"Vigilant Algorithmic Monitoring of Software"},{"_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","title":"Learning provably stabilizing neural controllers for discrete-time stochastic systems","alternative_title":["LNCS"]},{"type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"KrCh"}],"has_accepted_license":"1","date_created":"2023-12-10T23:00:58Z","publication":"Journal of the Royal Society, Interface","external_id":{"pmid":["38016637"]},"volume":20,"quality_controlled":"1","article_processing_charge":"Yes (in subscription journal)","article_type":"original","project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"}],"author":[{"full_name":"Tkadlec, Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","last_name":"Tkadlec","first_name":"Josef","orcid":"0000-0002-1097-9684"},{"first_name":"Kamran","last_name":"Kaveh","full_name":"Kaveh, Kamran"},{"full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee"},{"full_name":"Nowak, Martin A.","last_name":"Nowak","first_name":"Martin A."}],"file":[{"access_level":"open_access","creator":"dernst","file_id":"14673","checksum":"2eefab13127c7786dbd33303c482a004","date_created":"2023-12-11T11:10:32Z","date_updated":"2023-12-11T11:10:32Z","file_name":"2023_RoyalInterface_Tkadlec.pdf","file_size":1720243,"success":1,"relation":"main_file","content_type":"application/pdf"}],"pmid":1,"acknowledgement":"K.C. acknowledges support from the ERC CoG 863818(ForM-SMArt). J.T. is supported by Center for Foundations ofModern Computer Science (Charles Univ. project UNCE/SCI/004).","day":"29","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publisher":"The Royal Society","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Evolutionary dynamics of mutants that modify population structure","oa_version":"Published Version","date_published":"2023-11-29T00:00:00Z","publication_status":"published","doi":"10.1098/rsif.2023.0355","intvolume":"        20","citation":{"ista":"Tkadlec J, Kaveh K, Chatterjee K, Nowak MA. 2023. Evolutionary dynamics of mutants that modify population structure. Journal of the Royal Society, Interface. 20(208), 20230355.","apa":"Tkadlec, J., Kaveh, K., Chatterjee, K., &#38; Nowak, M. A. (2023). Evolutionary dynamics of mutants that modify population structure. <i>Journal of the Royal Society, Interface</i>. The Royal Society. <a href=\"https://doi.org/10.1098/rsif.2023.0355\">https://doi.org/10.1098/rsif.2023.0355</a>","mla":"Tkadlec, Josef, et al. “Evolutionary Dynamics of Mutants That Modify Population Structure.” <i>Journal of the Royal Society, Interface</i>, vol. 20, no. 208, 20230355, The Royal Society, 2023, doi:<a href=\"https://doi.org/10.1098/rsif.2023.0355\">10.1098/rsif.2023.0355</a>.","chicago":"Tkadlec, Josef, Kamran Kaveh, Krishnendu Chatterjee, and Martin A. Nowak. “Evolutionary Dynamics of Mutants That Modify Population Structure.” <i>Journal of the Royal Society, Interface</i>. The Royal Society, 2023. <a href=\"https://doi.org/10.1098/rsif.2023.0355\">https://doi.org/10.1098/rsif.2023.0355</a>.","short":"J. Tkadlec, K. Kaveh, K. Chatterjee, M.A. Nowak, Journal of the Royal Society, Interface 20 (2023).","ama":"Tkadlec J, Kaveh K, Chatterjee K, Nowak MA. Evolutionary dynamics of mutants that modify population structure. <i>Journal of the Royal Society, Interface</i>. 2023;20(208). doi:<a href=\"https://doi.org/10.1098/rsif.2023.0355\">10.1098/rsif.2023.0355</a>","ieee":"J. Tkadlec, K. Kaveh, K. Chatterjee, and M. A. Nowak, “Evolutionary dynamics of mutants that modify population structure,” <i>Journal of the Royal Society, Interface</i>, vol. 20, no. 208. The Royal Society, 2023."},"scopus_import":"1","file_date_updated":"2023-12-11T11:10:32Z","ddc":["000","570"],"article_number":"20230355","_id":"14657","date_updated":"2025-07-14T09:10:00Z","issue":"208","abstract":[{"lang":"eng","text":"Natural selection is usually studied between mutants that differ in reproductive rate, but are subject to the same population structure. Here we explore how natural selection acts on mutants that have the same reproductive rate, but different population structures. In our framework, population structure is given by a graph that specifies where offspring can disperse. The invading mutant disperses offspring on a different graph than the resident wild-type. We find that more densely connected dispersal graphs tend to increase the invader’s fixation probability, but the exact relationship between structure and fixation probability is subtle. We present three main results. First, we prove that if both invader and resident are on complete dispersal graphs, then removing a single edge in the invader’s dispersal graph reduces its fixation probability. Second, we show that for certain island models higher invader’s connectivity increases its fixation probability, but the magnitude of the effect depends on the exact layout of the connections. Third, we show that for lattices the effect of different connectivity is comparable to that of different fitness: for large population size, the invader’s fixation probability is either constant or exponentially small, depending on whether it is more or less connected than the resident."}],"year":"2023","month":"11","ec_funded":1,"status":"public","oa":1,"publication_identifier":{"eissn":["1742-5662"]}},{"_id":"14736","date_updated":"2025-07-14T09:10:01Z","abstract":[{"text":"Payment channel networks (PCNs) are a promising technology to improve the scalability of cryptocurrencies. PCNs, however, face the challenge that the frequent usage of certain routes may deplete channels in one direction, and hence prevent further transactions. In order to reap the full potential of PCNs, recharging and rebalancing mechanisms are required to provision channels, as well as an admission control logic to decide which transactions to reject in case capacity is insufficient. This paper presents a formal model of this optimisation problem. In particular, we consider an online algorithms perspective, where transactions arrive over time in an unpredictable manner. Our main contributions are competitive online algorithms which come with provable guarantees over time. We empirically evaluate our algorithms on randomly generated transactions to compare the average performance of our algorithms to our theoretical bounds. We also show how this model and approach differs from related problems in classic communication networks.","lang":"eng"}],"year":"2023","month":"12","ec_funded":1,"status":"public","publication_identifier":{"isbn":["9783031477539"],"eisbn":["9783031477546"],"eissn":["1611-3349"],"issn":["0302-9743"]},"oa_version":"None","date_published":"2023-12-01T00:00:00Z","publication_status":"published","conference":{"name":"FC: Financial Cryptography and Data Security","start_date":"2023-05-01","location":"Bol, Brac, Croatia","end_date":"2023-05-05"},"doi":"10.1007/978-3-031-47754-6_18","citation":{"ama":"Bastankhah M, Chatterjee K, Maddah-Ali MA, Schmid S, Svoboda J, Yeo MX. R2: Boosting liquidity in payment channel networks with online admission control. In: <i>27th International Conference on Financial Cryptography and Data Security</i>. Vol 13950. Springer Nature; 2023:309-325. doi:<a href=\"https://doi.org/10.1007/978-3-031-47754-6_18\">10.1007/978-3-031-47754-6_18</a>","ieee":"M. Bastankhah, K. Chatterjee, M. A. Maddah-Ali, S. Schmid, J. Svoboda, and M. X. Yeo, “R2: Boosting liquidity in payment channel networks with online admission control,” in <i>27th International Conference on Financial Cryptography and Data Security</i>, Bol, Brac, Croatia, 2023, vol. 13950, pp. 309–325.","short":"M. Bastankhah, K. Chatterjee, M.A. Maddah-Ali, S. Schmid, J. Svoboda, M.X. Yeo, in:, 27th International Conference on Financial Cryptography and Data Security, Springer Nature, 2023, pp. 309–325.","chicago":"Bastankhah, Mahsa, Krishnendu Chatterjee, Mohammad Ali Maddah-Ali, Stefan Schmid, Jakub Svoboda, and Michelle X Yeo. “R2: Boosting Liquidity in Payment Channel Networks with Online Admission Control.” In <i>27th International Conference on Financial Cryptography and Data Security</i>, 13950:309–25. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/978-3-031-47754-6_18\">https://doi.org/10.1007/978-3-031-47754-6_18</a>.","apa":"Bastankhah, M., Chatterjee, K., Maddah-Ali, M. A., Schmid, S., Svoboda, J., &#38; Yeo, M. X. (2023). R2: Boosting liquidity in payment channel networks with online admission control. In <i>27th International Conference on Financial Cryptography and Data Security</i> (Vol. 13950, pp. 309–325). Bol, Brac, Croatia: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-47754-6_18\">https://doi.org/10.1007/978-3-031-47754-6_18</a>","ista":"Bastankhah M, Chatterjee K, Maddah-Ali MA, Schmid S, Svoboda J, Yeo MX. 2023. R2: Boosting liquidity in payment channel networks with online admission control. 27th International Conference on Financial Cryptography and Data Security. FC: Financial Cryptography and Data Security, LNCS, vol. 13950, 309–325.","mla":"Bastankhah, Mahsa, et al. “R2: Boosting Liquidity in Payment Channel Networks with Online Admission Control.” <i>27th International Conference on Financial Cryptography and Data Security</i>, vol. 13950, Springer Nature, 2023, pp. 309–25, doi:<a href=\"https://doi.org/10.1007/978-3-031-47754-6_18\">10.1007/978-3-031-47754-6_18</a>."},"intvolume":"     13950","project":[{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications"}],"author":[{"full_name":"Bastankhah, Mahsa","first_name":"Mahsa","last_name":"Bastankhah"},{"first_name":"Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu"},{"last_name":"Maddah-Ali","first_name":"Mohammad Ali","full_name":"Maddah-Ali, Mohammad Ali"},{"full_name":"Schmid, Stefan","first_name":"Stefan","last_name":"Schmid"},{"full_name":"Svoboda, Jakub","id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","last_name":"Svoboda","orcid":"0000-0002-1419-3267","first_name":"Jakub"},{"full_name":"Yeo, Michelle X","first_name":"Michelle X","orcid":"0009-0001-3676-4809","id":"2D82B818-F248-11E8-B48F-1D18A9856A87","last_name":"Yeo"}],"acknowledgement":"Supported by the German Federal Ministry of Education and Research (BMBF), grant 16KISK020K (6G-RIC), 2021–2025, and ERC CoG 863818 (ForM-SMArt).","day":"01","alternative_title":["LNCS"],"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"R2: Boosting liquidity in payment channel networks with online admission control","type":"conference","language":[{"iso":"eng"}],"department":[{"_id":"KrCh"},{"_id":"KrPi"}],"date_created":"2024-01-08T09:30:22Z","page":"309-325","publication":"27th International Conference on Financial Cryptography and Data Security","quality_controlled":"1","volume":13950,"article_processing_charge":"No"},{"author":[{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee"},{"first_name":"Ehsan","last_name":"Kafshdar Goharshady","full_name":"Kafshdar Goharshady, Ehsan"},{"full_name":"Novotný, Petr","first_name":"Petr","last_name":"Novotný","id":"3CC3B868-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Zárevúcky, Jiří","first_name":"Jiří","last_name":"Zárevúcky"},{"full_name":"Zikelic, Dorde","orcid":"0000-0002-4681-1699","first_name":"Dorde","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","last_name":"Zikelic"}],"project":[{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020"},{"call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"file":[{"relation":"main_file","content_type":"application/pdf","success":1,"file_size":502522,"date_updated":"2024-01-16T08:11:24Z","file_name":"2023_FormalAspectsComputing_Chatterjee.pdf","date_created":"2024-01-16T08:11:24Z","checksum":"3bb133eeb27ec01649a9a36445d952d9","creator":"dernst","file_id":"14804","access_level":"open_access"}],"acknowledgement":"This research was partially supported by the ERC CoG (grant no. 863818; ForM-SMArt), the Czech Science Foundation (grant no. GA21-24711S), and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 665385.","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"23","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Association for Computing Machinery","title":"On lexicographic proof rules for probabilistic termination","type":"journal_article","department":[{"_id":"KrCh"}],"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Formal Aspects of Computing","date_created":"2024-01-10T09:27:43Z","keyword":["Theoretical Computer Science","Software"],"quality_controlled":"1","volume":35,"external_id":{"arxiv":["2108.02188"]},"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"10414"}]},"article_type":"original","article_processing_charge":"Yes (via OA deal)","article_number":"11","_id":"14778","issue":"2","arxiv":1,"abstract":[{"text":"We consider the almost-sure (a.s.) termination problem for probabilistic programs, which are a stochastic extension of classical imperative programs. Lexicographic ranking functions provide a sound and practical approach for termination of non-probabilistic programs, and their extension to probabilistic programs is achieved via lexicographic ranking supermartingales (LexRSMs). However, LexRSMs introduced in the previous work have a limitation that impedes their automation: all of their components have to be non-negative in all reachable states. This might result in a LexRSM not existing even for simple terminating programs. Our contributions are twofold. First, we introduce a generalization of LexRSMs that allows for some components to be negative. This standard feature of non-probabilistic termination proofs was hitherto not known to be sound in the probabilistic setting, as the soundness proof requires a careful analysis of the underlying stochastic process. Second, we present polynomial-time algorithms using our generalized LexRSMs for proving a.s. termination in broad classes of linear-arithmetic programs.","lang":"eng"}],"date_updated":"2025-07-14T09:10:10Z","year":"2023","month":"06","ec_funded":1,"status":"public","publication_identifier":{"issn":["0934-5043"],"eissn":["1433-299X"]},"oa":1,"oa_version":"Published Version","date_published":"2023-06-23T00:00:00Z","doi":"10.1145/3585391","publication_status":"published","intvolume":"        35","citation":{"short":"K. Chatterjee, E. Kafshdar Goharshady, P. Novotný, J. Zárevúcky, D. Zikelic, Formal Aspects of Computing 35 (2023).","ieee":"K. Chatterjee, E. Kafshdar Goharshady, P. Novotný, J. Zárevúcky, and D. Zikelic, “On lexicographic proof rules for probabilistic termination,” <i>Formal Aspects of Computing</i>, vol. 35, no. 2. Association for Computing Machinery, 2023.","ama":"Chatterjee K, Kafshdar Goharshady E, Novotný P, Zárevúcky J, Zikelic D. On lexicographic proof rules for probabilistic termination. <i>Formal Aspects of Computing</i>. 2023;35(2). doi:<a href=\"https://doi.org/10.1145/3585391\">10.1145/3585391</a>","chicago":"Chatterjee, Krishnendu, Ehsan Kafshdar Goharshady, Petr Novotný, Jiří Zárevúcky, and Dorde Zikelic. “On Lexicographic Proof Rules for Probabilistic Termination.” <i>Formal Aspects of Computing</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3585391\">https://doi.org/10.1145/3585391</a>.","mla":"Chatterjee, Krishnendu, et al. “On Lexicographic Proof Rules for Probabilistic Termination.” <i>Formal Aspects of Computing</i>, vol. 35, no. 2, 11, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3585391\">10.1145/3585391</a>.","ista":"Chatterjee K, Kafshdar Goharshady E, Novotný P, Zárevúcky J, Zikelic D. 2023. On lexicographic proof rules for probabilistic termination. Formal Aspects of Computing. 35(2), 11.","apa":"Chatterjee, K., Kafshdar Goharshady, E., Novotný, P., Zárevúcky, J., &#38; Zikelic, D. (2023). On lexicographic proof rules for probabilistic termination. <i>Formal Aspects of Computing</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3585391\">https://doi.org/10.1145/3585391</a>"},"file_date_updated":"2024-01-16T08:11:24Z","ddc":["000"]},{"date_published":"2023-06-26T00:00:00Z","oa_version":"Preprint","conference":{"location":"Washington, DC, United States","end_date":"2023-02-14","name":"AAAI: Conference on Artificial Intelligence","start_date":"2023-02-07"},"publication_status":"published","doi":"10.1609/aaai.v37i10.26407","intvolume":"        37","citation":{"short":"D. Zikelic, M. Lechner, T.A. Henzinger, K. Chatterjee, in:, Proceedings of the 37th AAAI Conference on Artificial Intelligence, Association for the Advancement of Artificial Intelligence, 2023, pp. 11926–11935.","ama":"Zikelic D, Lechner M, Henzinger TA, Chatterjee K. Learning control policies for stochastic systems with reach-avoid guarantees. In: <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i>. Vol 37. Association for the Advancement of Artificial Intelligence; 2023:11926-11935. doi:<a href=\"https://doi.org/10.1609/aaai.v37i10.26407\">10.1609/aaai.v37i10.26407</a>","ieee":"D. Zikelic, M. Lechner, T. A. Henzinger, and K. Chatterjee, “Learning control policies for stochastic systems with reach-avoid guarantees,” in <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i>, Washington, DC, United States, 2023, vol. 37, no. 10, pp. 11926–11935.","apa":"Zikelic, D., Lechner, M., Henzinger, T. A., &#38; Chatterjee, K. (2023). Learning control policies for stochastic systems with reach-avoid guarantees. In <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i> (Vol. 37, pp. 11926–11935). Washington, DC, United States: Association for the Advancement of Artificial Intelligence. <a href=\"https://doi.org/10.1609/aaai.v37i10.26407\">https://doi.org/10.1609/aaai.v37i10.26407</a>","mla":"Zikelic, Dorde, et al. “Learning Control Policies for Stochastic Systems with Reach-Avoid Guarantees.” <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i>, vol. 37, no. 10, Association for the Advancement of Artificial Intelligence, 2023, pp. 11926–35, doi:<a href=\"https://doi.org/10.1609/aaai.v37i10.26407\">10.1609/aaai.v37i10.26407</a>.","ista":"Zikelic D, Lechner M, Henzinger TA, Chatterjee K. 2023. Learning control policies for stochastic systems with reach-avoid guarantees. Proceedings of the 37th AAAI Conference on Artificial Intelligence. AAAI: Conference on Artificial Intelligence vol. 37, 11926–11935.","chicago":"Zikelic, Dorde, Mathias Lechner, Thomas A Henzinger, and Krishnendu Chatterjee. “Learning Control Policies for Stochastic Systems with Reach-Avoid Guarantees.” In <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i>, 37:11926–35. Association for the Advancement of Artificial Intelligence, 2023. <a href=\"https://doi.org/10.1609/aaai.v37i10.26407\">https://doi.org/10.1609/aaai.v37i10.26407</a>."},"_id":"14830","year":"2023","date_updated":"2025-07-14T09:10:02Z","arxiv":1,"issue":"10","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."}],"ec_funded":1,"month":"06","publication_identifier":{"eissn":["2374-3468"],"issn":["2159-5399"]},"status":"public","language":[{"iso":"eng"}],"department":[{"_id":"ToHe"},{"_id":"KrCh"}],"type":"conference","date_created":"2024-01-18T07:44:31Z","page":"11926-11935","publication":"Proceedings of the 37th AAAI Conference on Artificial Intelligence","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"14600"}]},"external_id":{"arxiv":["2210.05308"]},"quality_controlled":"1","volume":37,"keyword":["General Medicine"],"article_processing_charge":"No","project":[{"call_identifier":"H2020","name":"Vigilant Algorithmic Monitoring of Software","_id":"62781420-2b32-11ec-9570-8d9b63373d4d","grant_number":"101020093"},{"_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program"}],"author":[{"first_name":"Dorde","orcid":"0000-0002-4681-1699","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","last_name":"Zikelic","full_name":"Zikelic, Dorde"},{"last_name":"Lechner","id":"3DC22916-F248-11E8-B48F-1D18A9856A87","first_name":"Mathias","full_name":"Lechner, Mathias"},{"full_name":"Henzinger, Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","orcid":"0000-0002-2985-7724","first_name":"Thomas A"},{"last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"}],"day":"26","acknowledgement":"This work was supported in part by the ERC-2020-AdG 101020093, ERC CoG 863818 (FoRM-SMArt) and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385.","title":"Learning control policies for stochastic systems with reach-avoid guarantees","publisher":"Association for the Advancement of Artificial Intelligence","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"month":"12","ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","oa":1,"title":"Compositional policy learning in stochastic control systems with formal guarantees","author":[{"orcid":"0000-0002-4681-1699","first_name":"Dorde","last_name":"Zikelic","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","full_name":"Zikelic, Dorde"},{"full_name":"Lechner, Mathias","last_name":"Lechner","id":"3DC22916-F248-11E8-B48F-1D18A9856A87","first_name":"Mathias"},{"first_name":"Abhinav","last_name":"Verma","id":"a235593c-d7fa-11eb-a0c5-b22ca3c66ee6","full_name":"Verma, Abhinav"},{"last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"full_name":"Henzinger, Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","first_name":"Thomas A","orcid":"0000-0002-2985-7724"}],"project":[{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications"},{"grant_number":"101020093","_id":"62781420-2b32-11ec-9570-8d9b63373d4d","name":"Vigilant Algorithmic Monitoring of Software","call_identifier":"H2020"}],"_id":"15023","acknowledgement":"This work was supported in part by the ERC-2020-AdG 101020093 (VAMOS) and the ERC-2020-\r\nCoG 863818 (FoRM-SMArt).","arxiv":1,"abstract":[{"text":"Reinforcement learning has shown promising results in learning neural network policies for complicated control tasks. However, the lack of formal guarantees about the behavior of such policies remains an impediment to their deployment. We propose a novel method for learning a composition of neural network policies in stochastic environments, along with a formal certificate which guarantees that a specification over the policy's behavior is satisfied with the desired probability. Unlike prior work on verifiable RL, our approach leverages the compositional nature of logical specifications provided in SpectRL, to learn over graphs of probabilistic reach-avoid specifications. The formal guarantees are provided by learning neural network policies together with reach-avoid supermartingales (RASM) for the graph’s sub-tasks and then composing them into a global policy. We also derive a tighter lower bound compared to previous work on the probability of reach-avoidance implied by a RASM, which is required to find a compositional policy with an acceptable probabilistic threshold for complex tasks with multiple edge policies. We implement a prototype of our approach and evaluate it on a Stochastic Nine Rooms environment.","lang":"eng"}],"date_updated":"2025-07-14T09:10:04Z","year":"2023","day":"15","citation":{"ama":"Zikelic D, Lechner M, Verma A, Chatterjee K, Henzinger TA. Compositional policy learning in stochastic control systems with formal guarantees. In: <i>37th Conference on Neural Information Processing Systems</i>. ; 2023.","ieee":"D. Zikelic, M. Lechner, A. Verma, K. Chatterjee, and T. A. Henzinger, “Compositional policy learning in stochastic control systems with formal guarantees,” in <i>37th Conference on Neural Information Processing Systems</i>, New Orleans, LO, United States, 2023.","short":"D. Zikelic, M. Lechner, A. Verma, K. Chatterjee, T.A. Henzinger, in:, 37th Conference on Neural Information Processing Systems, 2023.","chicago":"Zikelic, Dorde, Mathias Lechner, Abhinav Verma, Krishnendu Chatterjee, and Thomas A Henzinger. “Compositional Policy Learning in Stochastic Control Systems with Formal Guarantees.” In <i>37th Conference on Neural Information Processing Systems</i>, 2023.","ista":"Zikelic D, Lechner M, Verma A, Chatterjee K, Henzinger TA. 2023. Compositional policy learning in stochastic control systems with formal guarantees. 37th Conference on Neural Information Processing Systems. NeurIPS: Neural Information Processing Systems.","apa":"Zikelic, D., Lechner, M., Verma, A., Chatterjee, K., &#38; Henzinger, T. A. (2023). Compositional policy learning in stochastic control systems with formal guarantees. In <i>37th Conference on Neural Information Processing Systems</i>. New Orleans, LO, United States.","mla":"Zikelic, Dorde, et al. “Compositional Policy Learning in Stochastic Control Systems with Formal Guarantees.” <i>37th Conference on Neural Information Processing Systems</i>, 2023."},"quality_controlled":"1","external_id":{"arxiv":["2312.01456"]},"article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2312.01456","open_access":"1"}],"type":"conference","oa_version":"Preprint","department":[{"_id":"ToHe"},{"_id":"KrCh"}],"date_published":"2023-12-15T00:00:00Z","language":[{"iso":"eng"}],"conference":{"start_date":"2023-12-10","name":"NeurIPS: Neural Information Processing Systems","end_date":"2023-12-16","location":"New Orleans, LO, United States"},"publication_status":"epub_ahead","publication":"37th Conference on Neural Information Processing Systems","date_created":"2024-02-25T09:23:24Z"},{"author":[{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee"},{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","first_name":"Thomas A","orcid":"0000-0002-2985-7724","full_name":"Henzinger, Thomas A"},{"full_name":"Lechner, Mathias","first_name":"Mathias","last_name":"Lechner","id":"3DC22916-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Zikelic, Dorde","orcid":"0000-0002-4681-1699","first_name":"Dorde","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","last_name":"Zikelic"}],"project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"}],"file":[{"content_type":"application/pdf","relation":"main_file","success":1,"file_size":528455,"file_name":"2023_LNCS_Chatterjee.pdf","date_updated":"2023-06-19T08:29:30Z","date_created":"2023-06-19T08:29:30Z","checksum":"3d8a8bb24d211bc83360dfc2fd744307","creator":"dernst","file_id":"13150","access_level":"open_access"}],"acknowledgement":"This work was supported in part by the ERC-2020-AdG 101020093, ERC CoG 863818 (FoRM-SMArt) and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385.","day":"22","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"alternative_title":["LNCS"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","title":"A learner-verifier framework for neural network controllers and certificates of stochastic systems","type":"conference","department":[{"_id":"KrCh"},{"_id":"ToHe"}],"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Tools and Algorithms for the Construction and Analysis of Systems ","date_created":"2023-06-18T22:00:47Z","page":"3-25","volume":13993,"quality_controlled":"1","article_processing_charge":"No","_id":"13142","abstract":[{"lang":"eng","text":"Reinforcement learning has received much attention for learning controllers of deterministic systems. We consider a learner-verifier framework for stochastic control systems and survey recent methods that formally guarantee a conjunction of reachability and safety properties. Given a property and a lower bound on the probability of the property being satisfied, our framework jointly learns a control policy and a formal certificate to ensure the satisfaction of the property with a desired probability threshold. Both the control policy and the formal certificate are continuous functions from states to reals, which are learned as parameterized neural networks. While in the deterministic case, the certificates are invariant and barrier functions for safety, or Lyapunov and ranking functions for liveness, in the stochastic case the certificates are supermartingales. For certificate verification, we use interval arithmetic abstract interpretation to bound the expected values of neural network functions."}],"date_updated":"2025-07-14T09:09:52Z","year":"2023","month":"04","ec_funded":1,"status":"public","oa":1,"publication_identifier":{"eissn":["1611-3349"],"isbn":["9783031308222"],"issn":["0302-9743"]},"oa_version":"Published Version","date_published":"2023-04-22T00:00:00Z","doi":"10.1007/978-3-031-30823-9_1","publication_status":"published","conference":{"end_date":"2023-04-27","location":"Paris, France","start_date":"2023-04-22","name":"TACAS: Tools and Algorithms for the Construction and Analysis of Systems"},"intvolume":"     13993","citation":{"ama":"Chatterjee K, Henzinger TA, Lechner M, Zikelic D. A learner-verifier framework for neural network controllers and certificates of stochastic systems. In: <i>Tools and Algorithms for the Construction and Analysis of Systems </i>. Vol 13993. Springer Nature; 2023:3-25. doi:<a href=\"https://doi.org/10.1007/978-3-031-30823-9_1\">10.1007/978-3-031-30823-9_1</a>","ieee":"K. Chatterjee, T. A. Henzinger, M. Lechner, and D. Zikelic, “A learner-verifier framework for neural network controllers and certificates of stochastic systems,” in <i>Tools and Algorithms for the Construction and Analysis of Systems </i>, Paris, France, 2023, vol. 13993, pp. 3–25.","short":"K. Chatterjee, T.A. Henzinger, M. Lechner, D. Zikelic, in:, Tools and Algorithms for the Construction and Analysis of Systems , Springer Nature, 2023, pp. 3–25.","mla":"Chatterjee, Krishnendu, et al. “A Learner-Verifier Framework for Neural Network Controllers and Certificates of Stochastic Systems.” <i>Tools and Algorithms for the Construction and Analysis of Systems </i>, vol. 13993, Springer Nature, 2023, pp. 3–25, doi:<a href=\"https://doi.org/10.1007/978-3-031-30823-9_1\">10.1007/978-3-031-30823-9_1</a>.","ista":"Chatterjee K, Henzinger TA, Lechner M, Zikelic D. 2023. A learner-verifier framework for neural network controllers and certificates of stochastic systems. Tools and Algorithms for the Construction and Analysis of Systems . TACAS: Tools and Algorithms for the Construction and Analysis of Systems, LNCS, vol. 13993, 3–25.","apa":"Chatterjee, K., Henzinger, T. A., Lechner, M., &#38; Zikelic, D. (2023). A learner-verifier framework for neural network controllers and certificates of stochastic systems. In <i>Tools and Algorithms for the Construction and Analysis of Systems </i> (Vol. 13993, pp. 3–25). Paris, France: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-30823-9_1\">https://doi.org/10.1007/978-3-031-30823-9_1</a>","chicago":"Chatterjee, Krishnendu, Thomas A Henzinger, Mathias Lechner, and Dorde Zikelic. “A Learner-Verifier Framework for Neural Network Controllers and Certificates of Stochastic Systems.” In <i>Tools and Algorithms for the Construction and Analysis of Systems </i>, 13993:3–25. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/978-3-031-30823-9_1\">https://doi.org/10.1007/978-3-031-30823-9_1</a>."},"scopus_import":"1","file_date_updated":"2023-06-19T08:29:30Z","ddc":["000"]},{"doi":"10.1038/s41467-023-39625-9","publication_status":"published","oa_version":"Published Version","date_published":"2023-07-12T00:00:00Z","file_date_updated":"2023-07-31T11:32:36Z","scopus_import":"1","ddc":["000"],"citation":{"apa":"Kleshnina, M., Hilbe, C., Simsa, S., Chatterjee, K., &#38; Nowak, M. A. (2023). The effect of environmental information on evolution of cooperation in stochastic games. <i>Nature Communications</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41467-023-39625-9\">https://doi.org/10.1038/s41467-023-39625-9</a>","ista":"Kleshnina M, Hilbe C, Simsa S, Chatterjee K, Nowak MA. 2023. The effect of environmental information on evolution of cooperation in stochastic games. Nature Communications. 14, 4153.","mla":"Kleshnina, Maria, et al. “The Effect of Environmental Information on Evolution of Cooperation in Stochastic Games.” <i>Nature Communications</i>, vol. 14, 4153, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1038/s41467-023-39625-9\">10.1038/s41467-023-39625-9</a>.","chicago":"Kleshnina, Maria, Christian Hilbe, Stepan Simsa, Krishnendu Chatterjee, and Martin A. Nowak. “The Effect of Environmental Information on Evolution of Cooperation in Stochastic Games.” <i>Nature Communications</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1038/s41467-023-39625-9\">https://doi.org/10.1038/s41467-023-39625-9</a>.","short":"M. Kleshnina, C. Hilbe, S. Simsa, K. Chatterjee, M.A. Nowak, Nature Communications 14 (2023).","ieee":"M. Kleshnina, C. Hilbe, S. Simsa, K. Chatterjee, and M. A. Nowak, “The effect of environmental information on evolution of cooperation in stochastic games,” <i>Nature Communications</i>, vol. 14. Springer Nature, 2023.","ama":"Kleshnina M, Hilbe C, Simsa S, Chatterjee K, Nowak MA. The effect of environmental information on evolution of cooperation in stochastic games. <i>Nature Communications</i>. 2023;14. doi:<a href=\"https://doi.org/10.1038/s41467-023-39625-9\">10.1038/s41467-023-39625-9</a>"},"intvolume":"        14","abstract":[{"lang":"eng","text":"Many human interactions feature the characteristics of social dilemmas where individual actions have consequences for the group and the environment. The feedback between behavior and environment can be studied with the framework of stochastic games. In stochastic games, the state of the environment can change, depending on the choices made by group members. Past work suggests that such feedback can reinforce cooperative behaviors. In particular, cooperation can evolve in stochastic games even if it is infeasible in each separate repeated game. In stochastic games, participants have an interest in conditioning their strategies on the state of the environment. Yet in many applications, precise information about the state could be scarce. Here, we study how the availability of information (or lack thereof) shapes evolution of cooperation. Already for simple examples of two state games we find surprising effects. In some cases, cooperation is only possible if there is precise information about the state of the environment. In other cases, cooperation is most abundant when there is no information about the state of the environment. We systematically analyze all stochastic games of a given complexity class, to determine when receiving information about the environment is better, neutral, or worse for evolution of cooperation."}],"date_updated":"2025-07-14T09:09:53Z","year":"2023","article_number":"4153","_id":"13258","status":"public","oa":1,"publication_identifier":{"eissn":["2041-1723"]},"month":"07","ec_funded":1,"has_accepted_license":"1","publication":"Nature Communications","date_created":"2023-07-23T22:01:11Z","type":"journal_article","department":[{"_id":"KrCh"}],"language":[{"iso":"eng"}],"article_processing_charge":"Yes","article_type":"original","quality_controlled":"1","volume":14,"external_id":{"isi":["001029450400031"],"pmid":["37438341"]},"related_material":{"record":[{"id":"13336","relation":"research_data","status":"public"}]},"acknowledgement":"This work was supported by the European Research Council CoG 863818 (ForM-SMArt) (to K.C.), the European Research Council Starting Grant 850529: E-DIRECT (to C.H.), the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement #754411 and the French Agence Nationale de la Recherche (under the Investissement d’Avenir programme, ANR-17-EURE-0010) (to M.K.).","pmid":1,"day":"12","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"author":[{"last_name":"Kleshnina","id":"4E21749C-F248-11E8-B48F-1D18A9856A87","first_name":"Maria","full_name":"Kleshnina, Maria"},{"full_name":"Hilbe, Christian","first_name":"Christian","orcid":"0000-0001-5116-955X","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","last_name":"Hilbe"},{"orcid":"0000-0001-6687-1210","first_name":"Stepan","id":"409d615c-2f95-11ee-b934-90a352102c1e","last_name":"Simsa","full_name":"Simsa, Stepan"},{"orcid":"0000-0002-4561-241X","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu"},{"first_name":"Martin A.","last_name":"Nowak","full_name":"Nowak, Martin A."}],"isi":1,"project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"},{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"file":[{"date_created":"2023-07-31T11:32:36Z","date_updated":"2023-07-31T11:32:36Z","file_name":"2023_NatureComm_Kleshnina.pdf","access_level":"open_access","checksum":"5aceefdfe76686267b93ae4fe81899f1","file_id":"13337","creator":"dernst","file_size":1601682,"success":1,"relation":"main_file","content_type":"application/pdf"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","title":"The effect of environmental information on evolution of cooperation in stochastic games"},{"type":"conference","department":[{"_id":"ToHe"},{"_id":"KrCh"}],"language":[{"iso":"eng"}],"publication":"Proceedings of the 37th AAAI Conference on Artificial Intelligence","page":"14964-14973","date_created":"2023-08-27T22:01:17Z","quality_controlled":"1","volume":37,"external_id":{"arxiv":["2211.16187"]},"article_processing_charge":"No","author":[{"last_name":"Lechner","id":"3DC22916-F248-11E8-B48F-1D18A9856A87","first_name":"Mathias","full_name":"Lechner, Mathias"},{"orcid":"0000-0002-4681-1699","first_name":"Dorde","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","last_name":"Zikelic","full_name":"Zikelic, Dorde"},{"full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","first_name":"Krishnendu"},{"full_name":"Henzinger, Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","first_name":"Thomas A","orcid":"0000-0002-2985-7724"},{"first_name":"Daniela","last_name":"Rus","full_name":"Rus, Daniela"}],"project":[{"name":"Vigilant Algorithmic Monitoring of Software","call_identifier":"H2020","grant_number":"101020093","_id":"62781420-2b32-11ec-9570-8d9b63373d4d"},{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"},{"call_identifier":"H2020","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385"}],"acknowledgement":"This work was supported in part by the ERC-2020-AdG 101020093, ERC CoG 863818 (FoRM-SMArt) and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385. Research was sponsored by the United\r\nStates Air Force Research Laboratory and the United States Air Force Artificial Intelligence Accelerator and was accomplished under Cooperative Agreement Number FA8750-19-2-\r\n1000. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied,\r\nof the United States Air Force or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright\r\nnotation herein. The research was also funded in part by the AI2050 program at Schmidt Futures (Grant G-22-63172) and Capgemini SE.","day":"26","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Association for the Advancement of Artificial Intelligence","title":"Quantization-aware interval bound propagation for training certifiably robust quantized neural networks","oa_version":"Preprint","date_published":"2023-06-26T00:00:00Z","doi":"10.1609/aaai.v37i12.26747","conference":{"name":"AAAI: Conference on Artificial Intelligence","start_date":"2023-02-07","location":"Washington, DC, United States","end_date":"2023-02-14"},"publication_status":"published","citation":{"ista":"Lechner M, Zikelic D, Chatterjee K, Henzinger TA, Rus D. 2023. Quantization-aware interval bound propagation for training certifiably robust quantized neural networks. Proceedings of the 37th AAAI Conference on Artificial Intelligence. AAAI: Conference on Artificial Intelligence vol. 37, 14964–14973.","mla":"Lechner, Mathias, et al. “Quantization-Aware Interval Bound Propagation for Training Certifiably Robust Quantized Neural Networks.” <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i>, vol. 37, no. 12, Association for the Advancement of Artificial Intelligence, 2023, pp. 14964–73, doi:<a href=\"https://doi.org/10.1609/aaai.v37i12.26747\">10.1609/aaai.v37i12.26747</a>.","apa":"Lechner, M., Zikelic, D., Chatterjee, K., Henzinger, T. A., &#38; Rus, D. (2023). Quantization-aware interval bound propagation for training certifiably robust quantized neural networks. In <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i> (Vol. 37, pp. 14964–14973). Washington, DC, United States: Association for the Advancement of Artificial Intelligence. <a href=\"https://doi.org/10.1609/aaai.v37i12.26747\">https://doi.org/10.1609/aaai.v37i12.26747</a>","chicago":"Lechner, Mathias, Dorde Zikelic, Krishnendu Chatterjee, Thomas A Henzinger, and Daniela Rus. “Quantization-Aware Interval Bound Propagation for Training Certifiably Robust Quantized Neural Networks.” In <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i>, 37:14964–73. Association for the Advancement of Artificial Intelligence, 2023. <a href=\"https://doi.org/10.1609/aaai.v37i12.26747\">https://doi.org/10.1609/aaai.v37i12.26747</a>.","short":"M. Lechner, D. Zikelic, K. Chatterjee, T.A. Henzinger, D. Rus, in:, Proceedings of the 37th AAAI Conference on Artificial Intelligence, Association for the Advancement of Artificial Intelligence, 2023, pp. 14964–14973.","ieee":"M. Lechner, D. Zikelic, K. Chatterjee, T. A. Henzinger, and D. Rus, “Quantization-aware interval bound propagation for training certifiably robust quantized neural networks,” in <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i>, Washington, DC, United States, 2023, vol. 37, no. 12, pp. 14964–14973.","ama":"Lechner M, Zikelic D, Chatterjee K, Henzinger TA, Rus D. Quantization-aware interval bound propagation for training certifiably robust quantized neural networks. In: <i>Proceedings of the 37th AAAI Conference on Artificial Intelligence</i>. Vol 37. Association for the Advancement of Artificial Intelligence; 2023:14964-14973. doi:<a href=\"https://doi.org/10.1609/aaai.v37i12.26747\">10.1609/aaai.v37i12.26747</a>"},"intvolume":"        37","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2211.16187"}],"scopus_import":"1","_id":"14242","issue":"12","arxiv":1,"abstract":[{"lang":"eng","text":"We study the problem of training and certifying adversarially robust quantized neural networks (QNNs). Quantization is a technique for making neural networks more efficient by running them using low-bit integer arithmetic and is therefore commonly adopted in industry. Recent work has shown that floating-point neural networks that have been verified to be robust can become vulnerable to adversarial attacks after quantization, and certification of the quantized representation is necessary to guarantee robustness. In this work, we present quantization-aware interval bound propagation (QA-IBP), a novel method for training robust QNNs. Inspired by advances in robust learning of non-quantized networks, our training algorithm computes the gradient of an abstract representation of the actual network. Unlike existing approaches, our method can handle the discrete semantics of QNNs. Based on QA-IBP, we also develop a complete verification procedure for verifying the adversarial robustness of QNNs, which is guaranteed to terminate and produce a correct answer. Compared to existing approaches, the key advantage of our verification procedure is that it runs entirely on GPU or other accelerator devices. We demonstrate experimentally that our approach significantly outperforms existing methods and establish the new state-of-the-art for training and certifying the robustness of QNNs."}],"date_updated":"2025-07-14T09:09:56Z","year":"2023","month":"06","ec_funded":1,"status":"public","publication_identifier":{"isbn":["9781577358800"]},"oa":1},{"conference":{"location":"Florence, Italy","end_date":"2023-01-25","name":"SODA: Symposium on Discrete Algorithms","start_date":"2023-01-22"},"publication_status":"published","doi":"10.1137/1.9781611977554.ch173","date_published":"2023-02-01T00:00:00Z","oa_version":"Published Version","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1137/1.9781611977554.ch173"}],"citation":{"ama":"Chatterjee K, Meggendorfer T, Saona Urmeneta RJ, Svoboda J. Faster algorithm for turn-based stochastic games with bounded treewidth. In: <i>Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms</i>. Society for Industrial and Applied Mathematics; 2023:4590-4605. doi:<a href=\"https://doi.org/10.1137/1.9781611977554.ch173\">10.1137/1.9781611977554.ch173</a>","ieee":"K. Chatterjee, T. Meggendorfer, R. J. Saona Urmeneta, and J. Svoboda, “Faster algorithm for turn-based stochastic games with bounded treewidth,” in <i>Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms</i>, Florence, Italy, 2023, pp. 4590–4605.","short":"K. Chatterjee, T. Meggendorfer, R.J. Saona Urmeneta, J. Svoboda, in:, Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2023, pp. 4590–4605.","mla":"Chatterjee, Krishnendu, et al. “Faster Algorithm for Turn-Based Stochastic Games with Bounded Treewidth.” <i>Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms</i>, Society for Industrial and Applied Mathematics, 2023, pp. 4590–605, doi:<a href=\"https://doi.org/10.1137/1.9781611977554.ch173\">10.1137/1.9781611977554.ch173</a>.","apa":"Chatterjee, K., Meggendorfer, T., Saona Urmeneta, R. J., &#38; Svoboda, J. (2023). Faster algorithm for turn-based stochastic games with bounded treewidth. In <i>Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms</i> (pp. 4590–4605). Florence, Italy: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611977554.ch173\">https://doi.org/10.1137/1.9781611977554.ch173</a>","ista":"Chatterjee K, Meggendorfer T, Saona Urmeneta RJ, Svoboda J. 2023. Faster algorithm for turn-based stochastic games with bounded treewidth. Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 4590–4605.","chicago":"Chatterjee, Krishnendu, Tobias Meggendorfer, Raimundo J Saona Urmeneta, and Jakub Svoboda. “Faster Algorithm for Turn-Based Stochastic Games with Bounded Treewidth.” In <i>Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms</i>, 4590–4605. Society for Industrial and Applied Mathematics, 2023. <a href=\"https://doi.org/10.1137/1.9781611977554.ch173\">https://doi.org/10.1137/1.9781611977554.ch173</a>."},"year":"2023","date_updated":"2025-07-14T09:09:50Z","abstract":[{"text":"Turn-based stochastic games (aka simple stochastic games) are two-player zero-sum games played on directed graphs with probabilistic transitions. The goal of player-max is to maximize the probability to reach a target state against the adversarial player-min. These games lie in NP ∩ coNP and are among the rare combinatorial problems that belong to this complexity class for which the existence of polynomial-time algorithm is a major open question. While randomized sub-exponential time algorithm exists, all known deterministic algorithms require exponential time in the worst-case. An important open question has been whether faster algorithms can be obtained parametrized by the treewidth of the game graph. Even deterministic sub-exponential time algorithm for constant treewidth turn-based stochastic games has remain elusive. In this work our main result is a deterministic algorithm to solve turn-based stochastic games that, given a game with n states, treewidth at most t, and the bit-complexity of the probabilistic transition function log D, has running time O ((tn2 log D)t log n). In particular, our algorithm is quasi-polynomial time for games with constant or poly-logarithmic treewidth.","lang":"eng"}],"_id":"12676","publication_identifier":{"isbn":["9781611977554"]},"oa":1,"status":"public","ec_funded":1,"month":"02","page":"4590-4605","date_created":"2023-02-24T12:20:47Z","publication":"Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms","language":[{"iso":"eng"}],"department":[{"_id":"GradSch"},{"_id":"KrCh"}],"type":"conference","article_processing_charge":"No","quality_controlled":"1","day":"01","acknowledgement":"This research was partially supported by the ERC CoG 863818 (ForM-SMArt) grant.","project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"}],"author":[{"first_name":"Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu"},{"first_name":"Tobias","orcid":"0000-0002-1712-2165","last_name":"Meggendorfer","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","full_name":"Meggendorfer, Tobias"},{"first_name":"Raimundo J","orcid":"0000-0001-5103-038X","last_name":"Saona Urmeneta","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425","full_name":"Saona Urmeneta, Raimundo J"},{"orcid":"0000-0002-1419-3267","first_name":"Jakub","id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","last_name":"Svoboda","full_name":"Svoboda, Jakub"}],"title":"Faster algorithm for turn-based stochastic games with bounded treewidth","publisher":"Society for Industrial and Applied Mathematics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"citation":{"ama":"Chatterjee K, Katoen JP, Mohr S, Weininger M, Winkler T. Stochastic games with lexicographic objectives. <i>Formal Methods in System Design</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s10703-023-00411-4\">10.1007/s10703-023-00411-4</a>","ieee":"K. Chatterjee, J. P. Katoen, S. Mohr, M. Weininger, and T. Winkler, “Stochastic games with lexicographic objectives,” <i>Formal Methods in System Design</i>. Springer Nature, 2023.","short":"K. Chatterjee, J.P. Katoen, S. Mohr, M. Weininger, T. Winkler, Formal Methods in System Design (2023).","ista":"Chatterjee K, Katoen JP, Mohr S, Weininger M, Winkler T. 2023. Stochastic games with lexicographic objectives. Formal Methods in System Design.","apa":"Chatterjee, K., Katoen, J. P., Mohr, S., Weininger, M., &#38; Winkler, T. (2023). Stochastic games with lexicographic objectives. <i>Formal Methods in System Design</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10703-023-00411-4\">https://doi.org/10.1007/s10703-023-00411-4</a>","mla":"Chatterjee, Krishnendu, et al. “Stochastic Games with Lexicographic Objectives.” <i>Formal Methods in System Design</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s10703-023-00411-4\">10.1007/s10703-023-00411-4</a>.","chicago":"Chatterjee, Krishnendu, Joost P Katoen, Stefanie Mohr, Maximilian Weininger, and Tobias Winkler. “Stochastic Games with Lexicographic Objectives.” <i>Formal Methods in System Design</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s10703-023-00411-4\">https://doi.org/10.1007/s10703-023-00411-4</a>."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s10703-023-00411-4"}],"scopus_import":"1","ddc":["000"],"oa_version":"Published Version","date_published":"2023-03-08T00:00:00Z","publication_status":"epub_ahead","doi":"10.1007/s10703-023-00411-4","month":"03","ec_funded":1,"status":"public","publication_identifier":{"eissn":["1572-8102"]},"oa":1,"_id":"12738","date_updated":"2025-07-14T09:10:14Z","abstract":[{"text":"We study turn-based stochastic zero-sum games with lexicographic preferences over objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit both randomness as well as controllable and adversarial non-determinism. Lexicographic order allows one to consider multiple objectives with a strict preference order. To the best of our knowledge, stochastic games with lexicographic objectives have not been studied before. For a mixture of reachability and safety objectives, we show that deterministic lexicographically optimal strategies exist and memory is only required to remember the already satisfied and violated objectives. For a constant number of objectives, we show that the relevant decision problem is in NP∩coNP, matching the current known bound for single objectives; and in general the decision problem is PSPACE-hard and can be solved in NEXPTIME∩coNEXPTIME. We present an algorithm that computes the lexicographically optimal strategies via a reduction to the computation of optimal strategies in a sequence of single-objectives games. For omega-regular objectives, we restrict our analysis to one-player games, also known as Markov decision processes. We show that lexicographically optimal strategies exist and need either randomization or finite memory. We present an algorithm that solves the relevant decision problem in polynomial time. We have implemented our algorithms and report experimental results on various case studies.","lang":"eng"}],"year":"2023","external_id":{"isi":["000946174300001"]},"quality_controlled":"1","related_material":{"record":[{"id":"8272","status":"public","relation":"earlier_version"}]},"article_type":"original","article_processing_charge":"No","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"KrCh"}],"date_created":"2023-03-19T23:00:59Z","publication":"Formal Methods in System Design","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Stochastic games with lexicographic objectives","project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"},{"_id":"25892FC0-B435-11E9-9278-68D0E5697425","grant_number":"ICT15-003","name":"Efficient Algorithms for Computer Aided Verification"}],"isi":1,"author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"full_name":"Katoen, Joost P","first_name":"Joost P","last_name":"Katoen","id":"4524F760-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mohr, Stefanie","first_name":"Stefanie","last_name":"Mohr"},{"full_name":"Weininger, Maximilian","first_name":"Maximilian","last_name":"Weininger"},{"last_name":"Winkler","first_name":"Tobias","full_name":"Winkler, Tobias"}],"acknowledgement":"Tobias Winkler and Joost-Pieter Katoen are supported by the DFG RTG 2236 UnRAVeL and the innovation programme under the Marie Skłodowska-Curie grant agreement No. 101008233 (Mission). Krishnendu Chatterjee is supported by the ERC CoG 863818 (ForM-SMArt) and the Vienna Science and Technology Fund (WWTF) Project ICT15-003. Maximilian Weininger is supported by the DFG projects 383882557 Statistical Unbounded Verification (SUV) and 427755713 Group-By Objectives in Probabilistic Verification (GOPro). Stefanie Mohr is supported by the DFG RTG 2428 CONVEY. Open Access funding enabled and organized by Projekt DEAL.","day":"08","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}},{"has_accepted_license":"1","date_created":"2023-04-02T22:01:09Z","publication":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"KrCh"}],"article_processing_charge":"No","article_type":"original","external_id":{"isi":["000957125500002"]},"volume":479,"quality_controlled":"1","related_material":{"link":[{"relation":"research_data","url":"https://doi.org/10.6084/m9.figshare.21261771.v1"}]},"acknowledgement":"J.S. and K.C. acknowledge support from the ERC CoG 863818 (ForM-SMArt)","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"29","project":[{"_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020"}],"author":[{"first_name":"Jakub","orcid":"0000-0002-1419-3267","last_name":"Svoboda","id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","full_name":"Svoboda, Jakub"},{"first_name":"Josef","orcid":"0000-0002-1097-9684","last_name":"Tkadlec","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","full_name":"Tkadlec, Josef"},{"full_name":"Kaveh, Kamran","first_name":"Kamran","last_name":"Kaveh"},{"orcid":"0000-0002-4561-241X","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu"}],"isi":1,"file":[{"date_created":"2023-04-03T06:25:29Z","date_updated":"2023-04-03T06:25:29Z","file_name":"2023_ProceedingsRoyalSocietyA_Svoboda.pdf","access_level":"open_access","checksum":"13953d349fbefcb5d21ccc6b303297eb","creator":"dernst","file_id":"12796","success":1,"file_size":827784,"content_type":"application/pdf","relation":"main_file"}],"publisher":"The Royal Society","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Coexistence times in the Moran process with environmental heterogeneity","publication_status":"published","doi":"10.1098/rspa.2022.0685","oa_version":"Published Version","date_published":"2023-03-29T00:00:00Z","scopus_import":"1","file_date_updated":"2023-04-03T06:25:29Z","ddc":["000"],"intvolume":"       479","citation":{"ama":"Svoboda J, Tkadlec J, Kaveh K, Chatterjee K. Coexistence times in the Moran process with environmental heterogeneity. <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. 2023;479(2271). doi:<a href=\"https://doi.org/10.1098/rspa.2022.0685\">10.1098/rspa.2022.0685</a>","ieee":"J. Svoboda, J. Tkadlec, K. Kaveh, and K. Chatterjee, “Coexistence times in the Moran process with environmental heterogeneity,” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 479, no. 2271. The Royal Society, 2023.","short":"J. Svoboda, J. Tkadlec, K. Kaveh, K. Chatterjee, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 479 (2023).","chicago":"Svoboda, Jakub, Josef Tkadlec, Kamran Kaveh, and Krishnendu Chatterjee. “Coexistence Times in the Moran Process with Environmental Heterogeneity.” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. The Royal Society, 2023. <a href=\"https://doi.org/10.1098/rspa.2022.0685\">https://doi.org/10.1098/rspa.2022.0685</a>.","mla":"Svoboda, Jakub, et al. “Coexistence Times in the Moran Process with Environmental Heterogeneity.” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 479, no. 2271, 20220685, The Royal Society, 2023, doi:<a href=\"https://doi.org/10.1098/rspa.2022.0685\">10.1098/rspa.2022.0685</a>.","apa":"Svoboda, J., Tkadlec, J., Kaveh, K., &#38; Chatterjee, K. (2023). Coexistence times in the Moran process with environmental heterogeneity. <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. The Royal Society. <a href=\"https://doi.org/10.1098/rspa.2022.0685\">https://doi.org/10.1098/rspa.2022.0685</a>","ista":"Svoboda J, Tkadlec J, Kaveh K, Chatterjee K. 2023. Coexistence times in the Moran process with environmental heterogeneity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 479(2271), 20220685."},"date_updated":"2025-07-14T09:09:51Z","issue":"2271","abstract":[{"text":"Populations evolve in spatially heterogeneous environments. While a certain trait might bring a fitness advantage in some patch of the environment, a different trait might be advantageous in another patch. Here, we study the Moran birth–death process with two types of individuals in a population stretched across two patches of size N, each patch favouring one of the two types. We show that the long-term fate of such populations crucially depends on the migration rate μ\r\n between the patches. To classify the possible fates, we use the distinction between polynomial (short) and exponential (long) timescales. We show that when μ is high then one of the two types fixates on the whole population after a number of steps that is only polynomial in N. By contrast, when μ is low then each type holds majority in the patch where it is favoured for a number of steps that is at least exponential in N. Moreover, we precisely identify the threshold migration rate μ⋆ that separates those two scenarios, thereby exactly delineating the situations that support long-term coexistence of the two types. We also discuss the case of various cycle graphs and we present computer simulations that perfectly match our analytical results.","lang":"eng"}],"year":"2023","article_number":"20220685","_id":"12787","status":"public","oa":1,"publication_identifier":{"eissn":["1471-2946"],"issn":["1364-5021"]},"month":"03","ec_funded":1},{"quality_controlled":"1","volume":14,"external_id":{"isi":["001003644100020"],"pmid":["37045828"]},"article_type":"original","article_processing_charge":"No","department":[{"_id":"KrCh"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Nature Communications","date_created":"2023-04-23T22:01:03Z","has_accepted_license":"1","title":"Quantitative assessment can stabilize indirect reciprocity under imperfect information","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature","file":[{"success":1,"file_size":1786475,"relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"dernst","file_id":"12868","checksum":"a4b3b7b36fbef068cabf4fb99501fef6","date_created":"2023-04-25T09:13:53Z","file_name":"2023_NatureComm_Schmid.pdf","date_updated":"2023-04-25T09:13:53Z"}],"isi":1,"author":[{"full_name":"Schmid, Laura","id":"38B437DE-F248-11E8-B48F-1D18A9856A87","last_name":"Schmid","first_name":"Laura","orcid":"0000-0002-6978-7329"},{"full_name":"Ekbatani, Farbod","first_name":"Farbod","last_name":"Ekbatani"},{"full_name":"Hilbe, Christian","orcid":"0000-0001-5116-955X","first_name":"Christian","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87","last_name":"Hilbe"},{"orcid":"0000-0002-4561-241X","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu"}],"project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"},{"grant_number":"Z211","_id":"25F42A32-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"12","acknowledgement":"This work was supported by the European Research Council CoG 863818 (ForM-SMArt) (to K.C.) and the European Research Council Starting Grant 850529: E-DIRECT (to C.H.). L.S. received additional partial support by the Austrian Science Fund (FWF) under grant Z211-N23 (Wittgenstein Award), and also thanks the support by the Stochastic Analysis and Application Research Center (SAARC) under National Research Foundation of Korea grant NRF-2019R1A5A1028324. The authors additionally thank Stefan Schmid for providing access to his lab infrastructure at the University of Vienna for the purpose of collecting simulation data.","pmid":1,"citation":{"mla":"Schmid, Laura, et al. “Quantitative Assessment Can Stabilize Indirect Reciprocity under Imperfect Information.” <i>Nature Communications</i>, vol. 14, 2086, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1038/s41467-023-37817-x\">10.1038/s41467-023-37817-x</a>.","apa":"Schmid, L., Ekbatani, F., Hilbe, C., &#38; Chatterjee, K. (2023). Quantitative assessment can stabilize indirect reciprocity under imperfect information. <i>Nature Communications</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41467-023-37817-x\">https://doi.org/10.1038/s41467-023-37817-x</a>","ista":"Schmid L, Ekbatani F, Hilbe C, Chatterjee K. 2023. Quantitative assessment can stabilize indirect reciprocity under imperfect information. Nature Communications. 14, 2086.","chicago":"Schmid, Laura, Farbod Ekbatani, Christian Hilbe, and Krishnendu Chatterjee. “Quantitative Assessment Can Stabilize Indirect Reciprocity under Imperfect Information.” <i>Nature Communications</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1038/s41467-023-37817-x\">https://doi.org/10.1038/s41467-023-37817-x</a>.","ieee":"L. Schmid, F. Ekbatani, C. Hilbe, and K. Chatterjee, “Quantitative assessment can stabilize indirect reciprocity under imperfect information,” <i>Nature Communications</i>, vol. 14. Springer Nature, 2023.","ama":"Schmid L, Ekbatani F, Hilbe C, Chatterjee K. Quantitative assessment can stabilize indirect reciprocity under imperfect information. <i>Nature Communications</i>. 2023;14. doi:<a href=\"https://doi.org/10.1038/s41467-023-37817-x\">10.1038/s41467-023-37817-x</a>","short":"L. Schmid, F. Ekbatani, C. Hilbe, K. Chatterjee, Nature Communications 14 (2023)."},"intvolume":"        14","ddc":["000"],"scopus_import":"1","file_date_updated":"2023-04-25T09:13:53Z","date_published":"2023-04-12T00:00:00Z","oa_version":"Published Version","doi":"10.1038/s41467-023-37817-x","publication_status":"published","ec_funded":1,"month":"04","oa":1,"publication_identifier":{"eissn":["2041-1723"]},"status":"public","_id":"12861","article_number":"2086","year":"2023","abstract":[{"lang":"eng","text":"The field of indirect reciprocity investigates how social norms can foster cooperation when individuals continuously monitor and assess each other’s social interactions. By adhering to certain social norms, cooperating individuals can improve their reputation and, in turn, receive benefits from others. Eight social norms, known as the “leading eight,\" have been shown to effectively promote the evolution of cooperation as long as information is public and reliable. These norms categorize group members as either ’good’ or ’bad’. In this study, we examine a scenario where individuals instead assign nuanced reputation scores to each other, and only cooperate with those whose reputation exceeds a certain threshold. We find both analytically and through simulations that such quantitative assessments are error-correcting, thus facilitating cooperation in situations where information is private and unreliable. Moreover, our results identify four specific norms that are robust to such conditions, and may be relevant for helping to sustain cooperation in natural populations."}],"date_updated":"2025-07-14T09:09:52Z"},{"date_published":"2022-01-27T00:00:00Z","oa_version":"Published Version","doi":"10.1038/s41598-022-05333-5","publication_status":"published","intvolume":"        12","citation":{"chicago":"Svoboda, Jakub, Josef Tkadlec, Andreas Pavlogiannis, Krishnendu Chatterjee, and Martin A. Nowak. “Infection Dynamics of COVID-19 Virus under Lockdown and Reopening.” <i>Scientific Reports</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1038/s41598-022-05333-5\">https://doi.org/10.1038/s41598-022-05333-5</a>.","mla":"Svoboda, Jakub, et al. “Infection Dynamics of COVID-19 Virus under Lockdown and Reopening.” <i>Scientific Reports</i>, vol. 12, no. 1, 1526, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1038/s41598-022-05333-5\">10.1038/s41598-022-05333-5</a>.","ista":"Svoboda J, Tkadlec J, Pavlogiannis A, Chatterjee K, Nowak MA. 2022. Infection dynamics of COVID-19 virus under lockdown and reopening. Scientific Reports. 12(1), 1526.","apa":"Svoboda, J., Tkadlec, J., Pavlogiannis, A., Chatterjee, K., &#38; Nowak, M. A. (2022). Infection dynamics of COVID-19 virus under lockdown and reopening. <i>Scientific Reports</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41598-022-05333-5\">https://doi.org/10.1038/s41598-022-05333-5</a>","ieee":"J. Svoboda, J. Tkadlec, A. Pavlogiannis, K. Chatterjee, and M. A. Nowak, “Infection dynamics of COVID-19 virus under lockdown and reopening,” <i>Scientific Reports</i>, vol. 12, no. 1. Springer Nature, 2022.","ama":"Svoboda J, Tkadlec J, Pavlogiannis A, Chatterjee K, Nowak MA. Infection dynamics of COVID-19 virus under lockdown and reopening. <i>Scientific Reports</i>. 2022;12(1). doi:<a href=\"https://doi.org/10.1038/s41598-022-05333-5\">10.1038/s41598-022-05333-5</a>","short":"J. Svoboda, J. Tkadlec, A. Pavlogiannis, K. Chatterjee, M.A. Nowak, Scientific Reports 12 (2022)."},"ddc":["570"],"scopus_import":"1","file_date_updated":"2022-02-07T14:57:59Z","_id":"10731","article_number":"1526","year":"2022","arxiv":1,"abstract":[{"lang":"eng","text":"Motivated by COVID-19, we develop and analyze a simple stochastic model for the spread of disease in human population. We track how the number of infected and critically ill people develops over time in order to estimate the demand that is imposed on the hospital system. To keep this demand under control, we consider a class of simple policies for slowing down and reopening society and we compare their efficiency in mitigating the spread of the virus from several different points of view. We find that in order to avoid overwhelming of the hospital system, a policy must impose a harsh lockdown or it must react swiftly (or both). While reacting swiftly is universally beneficial, being harsh pays off only when the country is patient about reopening and when the neighboring countries coordinate their mitigation efforts. Our work highlights the importance of acting decisively when closing down and the importance of patience and coordination between neighboring countries when reopening."}],"issue":"1","date_updated":"2025-07-14T09:10:12Z","ec_funded":1,"month":"01","publication_identifier":{"eissn":["2045-2322"]},"oa":1,"status":"public","department":[{"_id":"KrCh"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Scientific Reports","date_created":"2022-02-06T23:01:30Z","has_accepted_license":"1","volume":12,"quality_controlled":"1","external_id":{"isi":["000749198000039"],"arxiv":["2012.15155"]},"article_type":"original","article_processing_charge":"No","file":[{"success":1,"file_size":2971922,"relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"alisjak","checksum":"247afd30c173390940f099ead35a28ed","file_id":"10744","date_created":"2022-02-07T14:57:59Z","date_updated":"2022-02-07T14:57:59Z","file_name":"2022_ScientificReports_Svoboda.pdf"}],"isi":1,"author":[{"full_name":"Svoboda, Jakub","first_name":"Jakub","orcid":"0000-0002-1419-3267","id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","last_name":"Svoboda"},{"last_name":"Tkadlec","first_name":"Josef","full_name":"Tkadlec, Josef"},{"first_name":"Andreas","orcid":"0000-0002-8943-0722","id":"49704004-F248-11E8-B48F-1D18A9856A87","last_name":"Pavlogiannis","full_name":"Pavlogiannis, Andreas"},{"full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee"},{"full_name":"Nowak, Martin A.","last_name":"Nowak","first_name":"Martin A."}],"project":[{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"27","acknowledgement":"K.C. acknowledges support from ERC Consolidator Grant No. (863818: ForM-SMart). A.P. acknowledges support from FWF Grant No. J-4220. M.A.N. acknowledges support from Office of Naval Research grant N00014-16-1-2914 and from the John Templeton Foundation.","title":"Infection dynamics of COVID-19 virus under lockdown and reopening","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature"},{"title":"Graph planning with expected finite horizon","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Elsevier","author":[{"full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","first_name":"Krishnendu"},{"full_name":"Doyen, Laurent","first_name":"Laurent","last_name":"Doyen"}],"isi":1,"project":[{"grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Game Theory"},{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications"}],"day":"01","acknowledgement":"This work was partially supported by Austrian Science Fund (FWF) NFN Grant No RiSE/SHiNE S11407 and by the grant ERC CoG 863818 (ForM-SMArt).","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"7402"}]},"quality_controlled":"1","volume":129,"external_id":{"arxiv":["1802.03642"],"isi":["000805002800001"]},"article_processing_charge":"No","article_type":"original","department":[{"_id":"KrCh"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Journal of Computer and System Sciences","page":"1-21","date_created":"2022-05-22T22:01:40Z","ec_funded":1,"month":"11","oa":1,"publication_identifier":{"issn":["0022-0000"],"eissn":["1090-2724"]},"status":"public","_id":"11402","year":"2022","arxiv":1,"abstract":[{"lang":"eng","text":"Fixed-horizon planning considers a weighted graph and asks to construct a path that maximizes the sum of weights for a given time horizon T. However, in many scenarios, the time horizon is not fixed, but the stopping time is chosen according to some distribution such that the expected stopping time is T. If the stopping-time distribution is not known, then to ensure robustness, the distribution is chosen by an adversary as the worst-case scenario. A stationary plan for every vertex always chooses the same outgoing edge. For fixed horizon or fixed stopping-time distribution, stationary plans are not sufficient for optimality. Quite surprisingly we show that when an adversary chooses the stopping-time distribution with expected stopping-time T, then stationary plans are sufficient. While computing optimal stationary plans for fixed horizon is NP-complete, we show that computing optimal stationary plans under adversarial stopping-time distribution can be achieved in polynomial time."}],"date_updated":"2025-07-14T09:09:54Z","citation":{"mla":"Chatterjee, Krishnendu, and Laurent Doyen. “Graph Planning with Expected Finite Horizon.” <i>Journal of Computer and System Sciences</i>, vol. 129, Elsevier, 2022, pp. 1–21, doi:<a href=\"https://doi.org/10.1016/j.jcss.2022.04.003\">10.1016/j.jcss.2022.04.003</a>.","apa":"Chatterjee, K., &#38; Doyen, L. (2022). Graph planning with expected finite horizon. <i>Journal of Computer and System Sciences</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jcss.2022.04.003\">https://doi.org/10.1016/j.jcss.2022.04.003</a>","ista":"Chatterjee K, Doyen L. 2022. Graph planning with expected finite horizon. Journal of Computer and System Sciences. 129, 1–21.","chicago":"Chatterjee, Krishnendu, and Laurent Doyen. “Graph Planning with Expected Finite Horizon.” <i>Journal of Computer and System Sciences</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jcss.2022.04.003\">https://doi.org/10.1016/j.jcss.2022.04.003</a>.","short":"K. Chatterjee, L. Doyen, Journal of Computer and System Sciences 129 (2022) 1–21.","ama":"Chatterjee K, Doyen L. Graph planning with expected finite horizon. <i>Journal of Computer and System Sciences</i>. 2022;129:1-21. doi:<a href=\"https://doi.org/10.1016/j.jcss.2022.04.003\">10.1016/j.jcss.2022.04.003</a>","ieee":"K. Chatterjee and L. Doyen, “Graph planning with expected finite horizon,” <i>Journal of Computer and System Sciences</i>, vol. 129. Elsevier, pp. 1–21, 2022."},"intvolume":"       129","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.1802.03642"}],"scopus_import":"1","date_published":"2022-11-01T00:00:00Z","oa_version":"Preprint","doi":"10.1016/j.jcss.2022.04.003","publication_status":"published"},{"main_file_link":[{"url":"https://arxiv.org/abs/2210.05308","open_access":"1"}],"article_processing_charge":"No","external_id":{"arxiv":["2210.05308"]},"citation":{"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>","ista":"Zikelic D, Lechner M, Henzinger TA, Chatterjee K. Learning control policies for stochastic systems with reach-avoid guarantees. arXiv, <a href=\"https://doi.org/10.48550/ARXIV.2210.05308\">10.48550/ARXIV.2210.05308</a>.","mla":"Zikelic, Dorde, et al. “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>.","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>.","short":"D. Zikelic, M. Lechner, T.A. Henzinger, K. Chatterjee, ArXiv (n.d.).","ieee":"D. Zikelic, M. Lechner, T. A. Henzinger, and K. Chatterjee, “Learning control policies for stochastic systems with reach-avoid guarantees,” <i>arXiv</i>. .","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>"},"related_material":{"record":[{"id":"14539","relation":"dissertation_contains","status":"public"},{"relation":"later_version","status":"public","id":"14830"}]},"publication_status":"submitted","doi":"10.48550/ARXIV.2210.05308","date_created":"2023-11-24T13:10:09Z","publication":"arXiv","type":"preprint","oa_version":"Preprint","language":[{"iso":"eng"}],"date_published":"2022-11-29T00:00:00Z","department":[{"_id":"KrCh"},{"_id":"ToHe"}],"status":"public","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","title":"Learning control policies for stochastic systems with reach-avoid guarantees","oa":1,"month":"11","ec_funded":1,"license":"https://creativecommons.org/licenses/by-sa/4.0/","date_updated":"2025-07-14T09:10:02Z","arxiv":1,"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."}],"day":"29","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","image":"/images/cc_by_sa.png","short":"CC BY-SA (4.0)"},"year":"2022","project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"},{"_id":"62781420-2b32-11ec-9570-8d9b63373d4d","grant_number":"101020093","call_identifier":"H2020","name":"Vigilant Algorithmic Monitoring of Software"},{"call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"author":[{"last_name":"Zikelic","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4681-1699","first_name":"Dorde","full_name":"Zikelic, Dorde"},{"full_name":"Lechner, Mathias","id":"3DC22916-F248-11E8-B48F-1D18A9856A87","last_name":"Lechner","first_name":"Mathias"},{"full_name":"Henzinger, Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","orcid":"0000-0002-2985-7724","first_name":"Thomas A"},{"last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"}],"_id":"14600"}]