{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/regularized-unconstrained-weakly-submodular","title":"Regularized Unconstrained Weakly Submodular Maximization","arxiv_id":"2408.04620","date":"2024-08-08","proceeding":null,"authors":["Yanhui Zhu","Samik Basu","A. Pavan"],"abstract":"Submodular optimization finds applications in machine learning and data mining. In this paper, we study the problem of maximizing functions of the form $h = f-c$, where $f$ is a monotone, non-negative, weakly submodular set function and $c$ is a modular function. We design a deterministic approximation algorithm that runs with ${{O}}(\\frac{n}{\\epsilon}\\log \\frac{n}{\\gamma \\epsilon})$ oracle calls to function $h$, and outputs a set ${S}$ such that $h({S}) \\geq \\gamma(1-\\epsilon)f(OPT)-c(OPT)-\\frac{c(OPT)}{\\gamma(1-\\epsilon)}\\log\\frac{f(OPT)}{c(OPT)}$, where $\\gamma$ is the submodularity ratio of $f$. Existing algorithms for this problem either admit a worse approximation ratio or have quadratic runtime. We also present an approximation ratio of our algorithm for this problem with an approximate oracle of $f$. We validate our theoretical results through extensive empirical evaluations on real-world applications, including vertex cover and influence diffusion problems for submodular utility function $f$, and Bayesian A-Optimal design for weakly submodular $f$. Our experimental results demonstrate that our algorithms efficiently achieve high-quality solutions.","url_abs":"https://arxiv.org/abs/2408.04620v2","url_pdf":"https://arxiv.org/pdf/2408.04620v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"regularized-unconstrained-weakly-submodular","repo_url":"https://github.com/yz24/UWSM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}