{"type":"ScholarlyArticle","title":"An Empirical Study of Branching Heuristics through the Lens of Global Learning Rate","authors":[{"name":"Jia Liang","slug":"jia-liang","given":"Jia","family":"Liang","affiliation":"University of Waterloo , Waterloo , Canada"},{"name":"Hari Govind","slug":"hari-govind","given":"Hari","family":"Govind","affiliation":"University of Waterloo , Waterloo , Canada"},{"name":"Pascal Poupart","slug":"pascal-poupart","given":"Pascal","family":"Poupart","affiliation":"University of Waterloo , Waterloo , Canada"},{"name":"Krzysztof Czarnecki","slug":"krzysztof-czarnecki","given":"Krzysztof","family":"Czarnecki","affiliation":"University of Waterloo , Waterloo , Canada"},{"name":"Vijay Ganesh","slug":"vijay-ganesh","given":"Vijay","family":"Ganesh","affiliation":"University of Waterloo , Waterloo , Canada"}],"abstract":"In this paper, we analyze a suite of 7 well-known branching heuristics proposed by the SAT community and show that the better heuristics tend to generate more learnt clauses per decision, a metric we define as the global learning rate (GLR). We propose GLR as a metric for the branching heuristic to optimize. We test our hypothesis by developing a new branching heuristic that maximizes GLR greedily. We show empirically that this heuristic achieves very high GLR and interestingly very low literal block distance (LBD) over the learnt clauses. In our experiments this greedy branching heuristic enables the solver to solve instances faster than VSIDS, when the branching time is taken out of the equation. This experiment is a good proof of concept that a branching heuristic maximizing GLR will lead to good solver performance modulo the computational overhead. Finally, we propose a new branching heuristic, called SGDB, that uses machine learning to cheapily approximate greedy maximization of GLR. We show experimentally that SGDB performs on par with the VSIDS branching heuristic.","doi":"10.24963/ijcai.2018/745","url":"https://ijcai.org/proceedings/2018/745","pdf":"https://ijcai.org/proceedings/2018/0745.pdf","markdown":"https://ijcai.org/proceedings/2018/745.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/745","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Sister Conferences Best Papers","track":"Best Sister Conferences","number":745,"pages":{"first":5319,"last":5323},"keywords":["Constraints and SAT: SAT","Heuristic Search and Game Playing: Heuristic Search and Machine Learning","Machine Learning: Machine Learning"],"videos":[],"references":[{"position":1,"raw":"[Audemard and Simon, 2009] Gilles Audemard and Laurent Simon. 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