{"type":"ScholarlyArticle","title":"Online Submodular Maximization via Adaptive Thresholds","authors":[{"name":"Zhengchen Yang","slug":"zhengchen-yang","given":"Zhengchen","family":"Yang","affiliation":"College of Computer Science & Technology , Nanjing University of Aeronautics & Astronautics , Nanjing , China"},{"name":"Jiping Zheng","slug":"jiping-zheng","given":"Jiping","family":"Zheng","affiliation":"College of Computer Science & Technology , Nanjing University of Aeronautics & Astronautics , Nanjing , China; State Key Laboratory for Novel Software Technology , Nanjing University , Nanjing , China"}],"abstract":"Submodular function maximization has been studied extensively in recent years due to its numerous applications in machine learning and artificial intelligence. We study a natural online variant of this problem on massive streaming data in which elements arrive one-by-one and the algorithm has to maintain a solution under cardinality constraint, i.e., k. Upon arrival of an element, the algorithm to maximize a monotone submodular function has to decide whether to accept the element and may replace a previously chosen element. Existing algorithms cannot simultaneously achieve optimal performance in terms of competitive ratio, memory complexity and running time. Also, the algorithm with best competitive ratio performs poorly in practice. In this paper, we propose a new algorithm OnlineAdaptive with optimal performance by exploiting adaptive thresholds to decide the acceptance of arriving elements by replacement. We prove that the competitive ratio of OnlineAdaptive is at least 1/4, and the ratio is about 0.2959 when k>=4 and approaches 0.3178 when k tends to infinity. In addition, OnlineAdaptive only needs O(k) memory and just performs one oracle per element. Experiments on diverse datasets confirm that OnlineAdaptive outperforms existing algorithms in both quality and efficiency.","doi":"10.24963/ijcai.2024/781","url":"https://ijcai.org/proceedings/2024/781","pdf":"https://ijcai.org/proceedings/2024/0781.pdf","markdown":"https://ijcai.org/proceedings/2024/781.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/781","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Search","track":"Main Track","number":781,"pages":{"first":7065,"last":7073},"keywords":["Search: S: Heuristic search","Search: S: Combinatorial search and optimisation"],"videos":[],"references":[{"position":1,"raw":"[Ashkan et al., 2015] Azin Ashkan, Branislav Kveton, Shlomo Berkovsky, and Zheng Wen. 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