{"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/local-saddle-point-optimization-a-curvature","title":"Local Saddle Point Optimization: A Curvature Exploitation Approach","arxiv_id":"1805.05751","date":"2018-05-15","proceeding":null,"authors":["Leonard Adolphs","Hadi Daneshmand","Aurelien Lucchi","Thomas Hofmann"],"abstract":"Gradient-based optimization methods are the most popular choice for finding\nlocal optima for classical minimization and saddle point problems. Here, we\nhighlight a systemic issue of gradient dynamics that arise for saddle point\nproblems, namely the presence of undesired stable stationary points that are no\nlocal optima. We propose a novel optimization approach that exploits curvature\ninformation in order to escape from these undesired stationary points. We prove\nthat different optimization methods, including gradient method and Adagrad,\nequipped with curvature exploitation can escape non-optimal stationary points.\nWe also provide empirical results on common saddle point problems which confirm\nthe advantage of using curvature exploitation.","url_abs":"http://arxiv.org/abs/1805.05751v3","url_pdf":"http://arxiv.org/pdf/1805.05751v3.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":"local-saddle-point-optimization-a-curvature","repo_url":"https://github.com/limcherhang/finalreport","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1805.05751","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}