{"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/a-new-branch-and-bound-pruning-framework-for","title":"A New Branch-and-Bound Pruning Framework for $\\ell_0$-Regularized Problems","arxiv_id":"2406.03504","date":"2024-06-03","proceeding":null,"authors":["Theo Guyard","Cédric Herzet","Clément Elvira","Ayşe-Nur Arslan"],"abstract":"We consider the resolution of learning problems involving $\\ell_0$-regularization via Branch-and-Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions through \"pruning tests\". In standard implementations, evaluating a pruning test requires to solve a convex optimization problem, which may result in computational bottlenecks. In this paper, we present an alternative to implement pruning tests for some generic family of $\\ell_0$-regularized problems. Our proposed procedure allows the simultaneous assessment of several regions and can be embedded in standard BnB implementations with a negligible computational overhead. We show through numerical simulations that our pruning strategy can improve the solving time of BnB procedures by several orders of magnitude for typical problems encountered in machine-learning applications.","url_abs":"https://arxiv.org/abs/2406.03504v1","url_pdf":"https://arxiv.org/pdf/2406.03504v1.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":"a-new-branch-and-bound-pruning-framework-for","repo_url":"https://github.com/TheoGuyard/El0ps","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"a-new-branch-and-bound-pruning-framework-for","repo_url":"https://github.com/TheoGuyard/l0exp","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[],"methods":[{"method_slug":"pruning","method_name":"Pruning"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2406.03504","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2406.03504"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/TheoGuyard/El0ps","reach":{"status":"ok","spdx":"GPL-3.0"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/TheoGuyard/l0exp","reach":{"status":"ok","spdx":"GPL-3.0"}}],"summary":{"unverified":1},"by_repo_kind":{"official":{"samples":1,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"fd3f1e81a2ed2860","entry":"compiled_clone","repo":"TheoGuyard/El0ps","repo_kind":"official","path":"src/el0ps/compilation.py","file_url":"https://github.com/TheoGuyard/El0ps/blob/HEAD/src/el0ps/compilation.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"GPL-3.0","inline_ok":false,"mcp_get_code":{"code_sha256":"fd3f1e81a2ed2860"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}