{"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/frank-wolfe-algorithms-for-saddle-point","title":"Frank-Wolfe Algorithms for Saddle Point Problems","arxiv_id":"1610.07797","date":"2016-10-25","proceeding":null,"authors":["Gauthier Gidel","Tony Jebara","Simon Lacoste-Julien"],"abstract":"We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained\nsmooth convex-concave saddle point (SP) problems. Remarkably, the method only\nrequires access to linear minimization oracles. Leveraging recent advances in\nFW optimization, we provide the first proof of convergence of a FW-type saddle\npoint solver over polytopes, thereby partially answering a 30 year-old\nconjecture. We also survey other convergence results and highlight gaps in the\ntheoretical underpinnings of FW-style algorithms. Motivating applications\nwithout known efficient alternatives are explored through structured prediction\nwith combinatorial penalties as well as games over matching polytopes involving\nan exponential number of constraints.","url_abs":"http://arxiv.org/abs/1610.07797v3","url_pdf":"http://arxiv.org/pdf/1610.07797v3.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":"frank-wolfe-algorithms-for-saddle-point","repo_url":"https://github.com/mustafakarabag/sp-admm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"frank-wolfe-algorithms-for-saddle-point","repo_url":"https://github.com/MindCode-4/code-12/tree/main/Frank-Wolfe-Algorithm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"frank-wolfe-algorithms-for-saddle-point","repo_url":"https://github.com/MindCode-4/code-7/tree/main/Frank-Wolfe-Algorithm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":null}],"tasks":[{"task_slug":"structured-prediction","task_name":"Structured Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1610.07797","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}