{"type":"ScholarlyArticle","title":"Learning-Based Abstractions for Nonlinear Constraint Solving","authors":[{"name":"Sumanth Dathathri","slug":"sumanth-dathathri","given":"Sumanth","family":"Dathathri","affiliation":"Computing and Mathematical Sciences , California Institute of Technology"},{"name":"Nikos Arechiga","slug":"nikos-arechiga","given":"Nikos","family":"Arechiga","affiliation":"Toyota InfoTechnology Center USA"},{"name":"Sicun Gao","slug":"sicun-gao","given":"Sicun","family":"Gao","affiliation":"Computer Science and Engineering , University of California , San Diego"},{"name":"Richard M. Murray","slug":"richard-m-murray","given":"Richard M.","family":"Murray","affiliation":"Computing and Mathematical Sciences , California Institute of Technology"}],"abstract":"We propose a new abstraction refinement procedure based on machine learning to improve the performance of nonlinear constraint solving algorithms on large-scale problems. The proposed approach decomposes the original set of constraints into smaller subsets, and uses learning algorithms to propose sequences of abstractions that take the form of conjunctions of classifiers. The core procedure is a refinement loop that keeps improving the learned results based on counterexamples that are obtained from partial constraints that are easy to solve. Experiments show that the proposed techniques significantly improve the performance of state-of-the-art constraint solvers on many challenging benchmarks. The mechanism is capable of producing intermediate symbolic abstractions that are also important for many applications and for understanding the internal structures of hard constraint solving problems.","doi":"10.24963/ijcai.2017/83","url":"https://ijcai.org/proceedings/2017/83","pdf":"https://ijcai.org/proceedings/2017/0083.pdf","markdown":"https://ijcai.org/proceedings/2017/83.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/83","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra, IIIA-CSIC","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Constraints and Satisfiability","track":"Main track","number":83,"pages":{"first":592,"last":599},"keywords":["Constraints and Satisfiability: Constraints and Satisfiability","Constraints and Satisfiability: Constraint Satisfaction","Constraints and Satisfiability: Satisfiability"],"videos":[],"references":[{"position":1,"raw":"[Albarghouthi and McMillan, 2013] Aws Albarghouthi and Kenneth L. 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