{"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/improved-regret-bounds-for-online-kernel","title":"Improved Regret Bounds for Online Kernel Selection under Bandit Feedback","arxiv_id":"2303.05018","date":"2023-03-09","proceeding":null,"authors":["Junfan Li","Shizhong Liao"],"abstract":"In this paper, we improve the regret bound for online kernel selection under bandit feedback. Previous algorithm enjoys a $O((\\Vert f\\Vert^2_{\\mathcal{H}_i}+1)K^{\\frac{1}{3}}T^{\\frac{2}{3}})$ expected bound for Lipschitz loss functions. We prove two types of regret bounds improving the previous bound. For smooth loss functions, we propose an algorithm with a $O(U^{\\frac{2}{3}}K^{-\\frac{1}{3}}(\\sum^K_{i=1}L_T(f^\\ast_i))^{\\frac{2}{3}})$ expected bound where $L_T(f^\\ast_i)$ is the cumulative losses of optimal hypothesis in $\\mathbb{H}_{i}=\\{f\\in\\mathcal{H}_i:\\Vert f\\Vert_{\\mathcal{H}_i}\\leq U\\}$. The data-dependent bound keeps the previous worst-case bound and is smaller if most of candidate kernels match well with the data. For Lipschitz loss functions, we propose an algorithm with a $O(U\\sqrt{KT}\\ln^{\\frac{2}{3}}{T})$ expected bound asymptotically improving the previous bound. We apply the two algorithms to online kernel selection with time constraint and prove new regret bounds matching or improving the previous $O(\\sqrt{T\\ln{K}} +\\Vert f\\Vert^2_{\\mathcal{H}_i}\\max\\{\\sqrt{T},\\frac{T}{\\sqrt{\\mathcal{R}}}\\})$ expected bound where $\\mathcal{R}$ is the time budget. Finally, we empirically verify our algorithms on online regression and classification tasks.","url_abs":"https://arxiv.org/abs/2303.05018v2","url_pdf":"https://arxiv.org/pdf/2303.05018v2.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":"improved-regret-bounds-for-online-kernel","repo_url":"https://github.com/junfli-tju/oks-bandit","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}