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Given a budget $M$ on the number of policy updates, in the first setting, the algorithm needs to decide upfront $M$ rounds at which it will update its policy, while in the second setting it can adaptively perform $M$ policy updates during its course. For the first setting, we design an algorithm $\\texttt{B-GLinCB}$, that incurs $\\tilde{O}(\\sqrt{T})$ regret when $M = \\Omega\\left( \\log{\\log T} \\right)$ and the arm feature vectors are generated stochastically. For the second setting, we design an algorithm $\\texttt{RS-GLinCB}$ that updates its policy $\\tilde{O}(\\log^2 T)$ times and achieves a regret of $\\tilde{O}(\\sqrt{T})$ even when the arm feature vectors are adversarially generated. Notably, in these bounds, we manage to eliminate the dependence on a key instance dependent parameter $\\kappa$, that captures non-linearity of the underlying reward model. Our novel approach for removing this dependence for generalized linear contextual bandits might be of independent interest.","url_abs":"https://arxiv.org/abs/2404.06831v3","url_pdf":"https://arxiv.org/pdf/2404.06831v3.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":"optimal-regret-with-limited-adaptivity-for","repo_url":"https://github.com/nirjhar-das/glbandit_limited_adaptivity","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"optimal-regret-with-limited-adaptivity-for","repo_url":"https://github.com/nick-jhlee/logistic_bandit","is_official":0,"mentioned_in_paper":0,"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":{"syntology_url":"https://syntology.ai/paper/2404.06831","atlas_url":"https://app.syntology.ai/?focus=2404.06831","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2404.06831"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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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