{"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/gradient-clipping-improves-adagrad-when-the","title":"Clipping Improves Adam-Norm and AdaGrad-Norm when the Noise Is Heavy-Tailed","arxiv_id":"2406.04443","date":"2024-06-06","proceeding":null,"authors":["Savelii Chezhegov","Yaroslav Klyukin","Andrei Semenov","Aleksandr Beznosikov","Alexander Gasnikov","Samuel Horváth","Martin Takáč","Eduard Gorbunov"],"abstract":"Methods with adaptive stepsizes, such as AdaGrad and Adam, are essential for training modern Deep Learning models, especially Large Language Models. Typically, the noise in the stochastic gradients is heavy-tailed for the later ones. Gradient clipping provably helps to achieve good high-probability convergence for such noises. However, despite the similarity between AdaGrad/Adam and Clip-SGD, the current understanding of the high-probability convergence of AdaGrad/Adam-type methods is limited in this case. In this work, we prove that AdaGrad/Adam (and their delayed version) can have provably bad high-probability convergence if the noise is heavy-tailed. We also show that gradient clipping fixes this issue, i.e., we derive new high-probability convergence bounds with polylogarithmic dependence on the confidence level for AdaGrad-Norm and Adam-Norm with clipping and with/without delay for smooth convex/non-convex stochastic optimization with heavy-tailed noise. Our empirical evaluations highlight the superiority of clipped versions of AdaGrad/Adam-Norm in handling the heavy-tailed noise.","url_abs":"https://arxiv.org/abs/2406.04443v2","url_pdf":"https://arxiv.org/pdf/2406.04443v2.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":"gradient-clipping-improves-adagrad-when-the","repo_url":"https://github.com/yaroslavkliukin/Clipped-AdaGrad-and-Adam","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[{"method_slug":"adagrad","method_name":"AdaGrad"},{"method_slug":"adam","method_name":"Adam"},{"method_slug":"gradient-clipping","method_name":"Gradient Clipping"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2406.04443","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}