{"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/kullback-leibler-maillard-sampling-for-multi","title":"Kullback-Leibler Maillard Sampling for Multi-armed Bandits with Bounded Rewards","arxiv_id":"2304.14989","date":"2023-04-28","proceeding":"NeurIPS 2023 11","authors":["Hao Qin","Kwang-Sung Jun","Chicheng Zhang"],"abstract":"We study $K$-armed bandit problems where the reward distributions of the arms are all supported on the $[0,1]$ interval. It has been a challenge to design regret-efficient randomized exploration algorithms in this setting. Maillard sampling \\cite{maillard13apprentissage}, an attractive alternative to Thompson sampling, has recently been shown to achieve competitive regret guarantees in the sub-Gaussian reward setting \\cite{bian2022maillard} while maintaining closed-form action probabilities, which is useful for offline policy evaluation. In this work, we propose the Kullback-Leibler Maillard Sampling (KL-MS) algorithm, a natural extension of Maillard sampling for achieving KL-style gap-dependent regret bound. We show that KL-MS enjoys the asymptotic optimality when the rewards are Bernoulli and has a worst-case regret bound of the form $O(\\sqrt{\\mu^*(1-\\mu^*) K T \\ln K} + K \\ln T)$, where $\\mu^*$ is the expected reward of the optimal arm, and $T$ is the time horizon length.","url_abs":"https://arxiv.org/abs/2304.14989v4","url_pdf":"https://arxiv.org/pdf/2304.14989v4.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":"kullback-leibler-maillard-sampling-for-multi","repo_url":"https://github.com/MjolnirT/Kullback-Leibler-Maillard-Sampling","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":"thompson-sampling","task_name":"Thompson Sampling"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2304.14989","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2304.14989"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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