{"type":"ScholarlyArticle","title":"Best Heuristic Identification for Constraint Satisfaction","authors":[{"name":"Frederic Koriche","slug":"frederic-koriche","given":"Frédéric","family":"Koriche","affiliation":"CRIL , Univ. Artois & CNRS"},{"name":"Christophe Lecoutre","slug":"christophe-lecoutre","given":"Christophe","family":"Lecoutre","affiliation":"CRIL , Univ. Artois & CNRS"},{"name":"Anastasia Paparrizou","slug":"anastasia-paparrizou","given":"Anastasia","family":"Paparrizou","affiliation":"CRIL , Univ. Artois & CNRS"},{"name":"Hugues Wattez","slug":"hugues-wattez","given":"Hugues","family":"Wattez","affiliation":"LIX CNRS , École Polytechnique , Institut Polytechnique de Paris"}],"abstract":"In constraint satisfaction problems, the variable ordering heuristic takes a central place by selecting the variables to branch on during backtrack search. As many hand-crafted branching heuristics have been proposed in the literature, a key issue is to identify, from a pool of candidate heuristics, which one is the best for solving a given constraint satisfaction task.  Based on the observation that modern constraint solvers are using restart sequences, the best heuristic identification problem can be cast in the context of multi-armed bandits as a non-stochastic best arm identification problem. Namely, during each run of some given restart sequence, the bandit algorithm selects a branching heuristic and receives a reward for this heuristic before proceeding to the next run. The goal is to identify the best heuristic using few runs, and without any stochastic assumption about the constraint solver. In this study, we propose an adaptive variant of Successive Halving that exploits Luby's universal restart sequence. We analyze the convergence of this bandit algorithm in the non-stochastic setting, \r\nand we demonstrate its empirical effectiveness on various constraint satisfaction benchmarks.","doi":"10.24963/ijcai.2022/258","url":"https://ijcai.org/proceedings/2022/258","pdf":"https://ijcai.org/proceedings/2022/0258.pdf","markdown":"https://ijcai.org/proceedings/2022/258.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/258","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Constraint Satisfaction and Optimization","track":"Main Track","number":258,"pages":{"first":1859,"last":1865},"keywords":["Constraint Satisfaction and Optimization: Constraint Satisfaction","Machine Learning: Reinforcement Learning","Constraint Satisfaction and Optimization: Constraints and Machine Learning"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38987058","length_sec":92,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985201","length_sec":725,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Audibert et al., 2010] Jean-Yves Audibert, Sébastien Bubeck, and Rémi Munos. 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