{"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/guarantees-for-greedy-maximization-of-non","title":"Guarantees for Greedy Maximization of Non-submodular Functions with Applications","arxiv_id":"1703.02100","date":"2017-03-06","proceeding":"ICML 2017 8","authors":["Andrew An Bian","Joachim M. Buhmann","Andreas Krause","Sebastian Tschiatschek"],"abstract":"We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for maximizing submodular functions, there are few guarantees for non-submodular ones. However, Greedy enjoys strong empirical performance for many important non-submodular functions, e.g., the Bayesian A-optimality objective in experimental design. We prove theoretical guarantees supporting the empirical performance. Our guarantees are characterized by a combination of the (generalized) curvature $\\alpha$ and the submodularity ratio $\\gamma$. In particular, we prove that Greedy enjoys a tight approximation guarantee of $\\frac{1}{\\alpha}(1- e^{-\\gamma\\alpha})$ for cardinality constrained maximization. In addition, we bound the submodularity ratio and curvature for several important real-world objectives, including the Bayesian A-optimality objective, the determinantal function of a square submatrix and certain linear programs with combinatorial constraints. We experimentally validate our theoretical findings for both synthetic and real-world applications.","url_abs":"https://arxiv.org/abs/1703.02100v4","url_pdf":"https://arxiv.org/pdf/1703.02100v4.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":"abstracts"},"code_links":[{"paper_slug":"guarantees-for-greedy-maximization-of-non","repo_url":"https://github.com/bianan/non-submodular-max","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"experimental-design","task_name":"Experimental Design"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1703.02100","atlas_url":"https://app.syntology.ai/?focus=1703.02100","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}