{"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/generalization-bounds-for-heavy-tailed-sdes","title":"Generalization Bounds for Heavy-Tailed SDEs through the Fractional Fokker-Planck Equation","arxiv_id":"2402.07723","date":"2024-02-12","proceeding":null,"authors":["Benjamin Dupuis","Umut Şimşekli"],"abstract":"Understanding the generalization properties of heavy-tailed stochastic optimization algorithms has attracted increasing attention over the past years. While illuminating interesting aspects of stochastic optimizers by using heavy-tailed stochastic differential equations as proxies, prior works either provided expected generalization bounds, or introduced non-computable information theoretic terms. Addressing these drawbacks, in this work, we prove high-probability generalization bounds for heavy-tailed SDEs which do not contain any nontrivial information theoretic terms. To achieve this goal, we develop new proof techniques based on estimating the entropy flows associated with the so-called fractional Fokker-Planck equation (a partial differential equation that governs the evolution of the distribution of the corresponding heavy-tailed SDE). In addition to obtaining high-probability bounds, we show that our bounds have a better dependence on the dimension of parameters as compared to prior art. Our results further identify a phase transition phenomenon, which suggests that heavy tails can be either beneficial or harmful depending on the problem structure. We support our theory with experiments conducted in a variety of settings.","url_abs":"https://arxiv.org/abs/2402.07723v2","url_pdf":"https://arxiv.org/pdf/2402.07723v2.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":"generalization-bounds-for-heavy-tailed-sdes","repo_url":"https://github.com/benjidupuis/heavy_tails_generalization","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"generalization-bounds","task_name":"Generalization Bounds"},{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2402.07723","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}