{"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/minimum-empirical-divergence-for-sub-gaussian","title":"Minimum Empirical Divergence for Sub-Gaussian Linear Bandits","arxiv_id":"2411.00229","date":"2024-10-31","proceeding":null,"authors":["Kapilan Balagopalan","Kwang-Sung Jun"],"abstract":"We propose a novel linear bandit algorithm called LinMED (Linear Minimum Empirical Divergence), which is a linear extension of the MED algorithm that was originally designed for multi-armed bandits. LinMED is a randomized algorithm that admits a closed-form computation of the arm sampling probabilities, unlike the popular randomized algorithm called linear Thompson sampling. Such a feature proves useful for off-policy evaluation where the unbiased evaluation requires accurately computing the sampling probability. We prove that LinMED enjoys a near-optimal regret bound of $d\\sqrt{n}$ up to logarithmic factors where $d$ is the dimension and $n$ is the time horizon. We further show that LinMED enjoys a $\\frac{d^2}{\\Delta}\\left(\\log^2(n)\\right)\\log\\left(\\log(n)\\right)$ problem-dependent regret where $\\Delta$ is the smallest sub-optimality gap, which is lower than $\\frac{d^2}{\\Delta}\\log^3(n)$ of the standard algorithm OFUL (Abbasi-yadkori et al., 2011). Our empirical study shows that LinMED has a competitive performance with the state-of-the-art algorithms.","url_abs":"https://arxiv.org/abs/2411.00229v1","url_pdf":"https://arxiv.org/pdf/2411.00229v1.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":"minimum-empirical-divergence-for-sub-gaussian","repo_url":"https://github.com/Kapilan-Balagopalan/Linear-Bandit-Algorithms","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"multi-armed-bandits","task_name":"Multi-Armed Bandits"},{"task_slug":"off-policy-evaluation","task_name":"Off-policy evaluation"},{"task_slug":"thompson-sampling","task_name":"Thompson Sampling"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}