{"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/implicitly-normalized-forecaster-with","title":"Implicitly normalized forecaster with clipping for linear and non-linear heavy-tailed multi-armed bandits","arxiv_id":"2305.06743","date":"2023-05-11","proceeding":null,"authors":["Yuriy Dorn","Nikita Kornilov","Nikolay Kutuzov","Alexander Nazin","Eduard Gorbunov","Alexander Gasnikov"],"abstract":"The Implicitly Normalized Forecaster (INF) algorithm is considered to be an optimal solution for adversarial multi-armed bandit (MAB) problems. However, most of the existing complexity results for INF rely on restrictive assumptions, such as bounded rewards. Recently, a related algorithm was proposed that works for both adversarial and stochastic heavy-tailed MAB settings. However, this algorithm fails to fully exploit the available data. In this paper, we propose a new version of INF called the Implicitly Normalized Forecaster with clipping (INF-clip) for MAB problems with heavy-tailed reward distributions. We establish convergence results under mild assumptions on the rewards distribution and demonstrate that INF-clip is optimal for linear heavy-tailed stochastic MAB problems and works well for non-linear ones. Furthermore, we show that INF-clip outperforms the best-of-both-worlds algorithm in cases where it is difficult to distinguish between different arms.","url_abs":"https://arxiv.org/abs/2305.06743v3","url_pdf":"https://arxiv.org/pdf/2305.06743v3.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":"implicitly-normalized-forecaster-with","repo_url":"https://github.com/kutuz4/implicitlynormalizedforecasterwithclipping","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"multi-armed-bandits","task_name":"Multi-Armed Bandits"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}