[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117273-en":3,"doc-seo-117273-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},117273,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Consistent Submodular Maximization - Proceedings (Machine Learning)","Maximizing monotone submodular functions under cardinality constraints is a classic optimization task with applications across data mining and machine learning. This work studies the problem in a streaming dynamic environment with consistency constraints: elements arrive sequentially, while the algorithm must maintain a constant approximation to the offline optimum and keep the solution stable, with bounded changes between consecutive steps. The paper proposes algorithms balancing consistency and approximation quality, and validates their effectiveness through experiments on real-world instances.","Consistent Submodular Maximization  \nPaul Dtting * 1 Federico Fusco * 2 Silvio Lattanzi * 1 Ashkan Norouzi-Fard * 1 Morteza Zadimoghaddam * 1  \nAbstract  \nMaximizing monotone submodular functions under cardinality constraints is a classic optimization task with several applications in data mining and machine learning. In this paper we study this problem in a dynamic environment with consistency constraints: elements arrive in a streaming fashion and the goal is maintaining a constant approximation to the optimal solution while having a stable solution (i.e., the number of changes between two consecutive solutions is bounded) . We provide algorithms in this setting with different trade-offs between consistency and approximation quality. We also complement our theoretical results with an experimental analysis showing the effectiveness of our algorithms in real-world instances.  \n1. Introduction  \nSubmodular optimization is a powerful framework for modeling and solving problems that exhibit the widespread diminishing returns property. Thanks to its effectiveness, it has been applied across diverse domains, including video analysis (Zheng et al., 2014), data summarization (Lin & Bilmes, 2011 ; Bairi et al., 2015), sparse reconstruction (Bach, 2010 ; Das & Kempe, 2011), and active learning (Golovin & Krause, 2011 ; Amanatidis et al., 2022) .  \nIn this paper, we focus on submodular maximization under cardinality constraints: given a submodular function f , a universe of elements V , and a cardinality constraint k , the goal is to find a set S of at most k elements that maximizes f(S) . Submodular maximization under cardinality constraints is NP-hard, nevertheless efficient approximation algorithms exist for this task in both the centralized and the streaming setting (Nemhauser et al., 1978 ; Badanidiyuru et al., 2014 ; Kazemi et al., 2019) .  \n*Equal contribution 1 Google Research 2 Sapienza University of Rome, Rome, Italy. Correspondence to: Federico Fusco \u003Cfed[erico.fusco@uniroma1.it](erico.fusco@uniroma1.it) > .  \nProceedings of the 41 st International Conference on Machine Learning, Vienna, Austria. PMLR 235, 2024 . Copyright 2024 by the author(s) .  \nOne aspect of efficient approximation algorithms for submodular maximization that has received little attention so far, is the stability of the solution. In fact, for some of the known algorithms, even adding a single element to the universe of elements V may completely change the final output (see Appendix A for some examples) . Unfortunately, this is problematic in many real-world applications where consistency is a fundamental system requirement. Indeed, a flurry of recent work has started to explore various optimization problems under stability and consistency constraints such as clustering (Lattanzi & Vassilvitskii, 2017 ; CohenAddad et al., 2022 ; Fichtenberger et al., 2021 ; Guo et al., 2021 ; Łacki et al., 2024), facility location (Cohen-Addad et al., 2019 ; Bhattacharya et al., 2022), and online learning (Jaghargh et al., 2019) .  \nHaving solutions that evolve smoothly is central in many practical application of submodular optimization. Consider, for example, the data summarization task in an evolving setting where elements are added to the universe V. In this setting, having a stable summary that changes as little as possible from step to step is very important both for serving the summary to a user or for using it in a machine learning model. In fact, in both settings a drastic change of the solution may have negative impact on system usability, it could harm user attention, and adversely effect the performance of the machine learning model.  \nFor these reasons, in this paper we initiate the study of submodular maximization under consistency constraints, where we allow the solutions to change only slightly after each element insertion. More formally, consider a stream V of exactly n elements, chosen by an adversary. Denote by Vt = fe1 ; : : : ; et g 􀀒 V the set of all element","cbCaigb49BdEtuEt","https://ap.wps.com/l/cbCaigb49BdEtuEt","pdf",472226,1,13,"English","en",105,"# Introduction\n## Submodular maximization with cardinality constraints\n## Stability and consistency in practical applications\n## Problem formulation and algorithmic goals\n## Related work and challenges","[{\"question\":\"What problem does the paper study?\",\"answer\":\"The paper studies maximizing monotone submodular functions under a cardinality constraint in a streaming (dynamic) setting while enforcing consistency of the maintained solution.\"},{\"question\":\"What are the two main requirements for the algorithm?\",\"answer\":\"It must maintain a constant-factor approximation to the optimum feasible solution after each insertion, and it must be C-consistent, meaning the number of elements changed between consecutive solutions is bounded.\"},{\"question\":\"Why is solution consistency important?\",\"answer\":\"In 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