Practical and Optimal Algorithm for Linear Contextual Bandits with Rare Parameter Updates

[2606.00984] Practical and Optimal Algorithm for Linear Contextual Bandits with Rare Parameter Updates Skip to main content Search Submit Donate Log in Statistics > Machine Learning arXiv:2606.00984 (stat) [Submitted on 31 May 2026 ( v1 ), last revised 22 Aug 2026 (this version, v3)] Title: Practical and Optimal Algorithm for Linear Contextual Bandits with Rare Parameter Updates Authors: Sanghoon Yu , Min-hwan Oh View PDF HTML (experimental) Abstract: We study linear contextual bandits under rare parameter updates: the learner may incorporate reward feedback into its parameter estimate only at a small number of update times, while still observing contexts online and selecting actions sequentially. This viewpoint clarifies a practical distinction that is often blurred in the literature: many "strictly batched" methods additionally restrict within-interval context adaptivity, meaning that the action rule inside an interval cannot depend on the sequence of realized contexts/actions in that interval (beyond the current round's context). For linear contextual bandits, we propose two practical algorithms with only $O(\log\log T)$ parameter updates. Our first algorithm BLCE-G attains minimax-optimal regret (up to polylogarithmic factors in $T$) simultaneously in both the small-$K$ and large-$K$ regimes under a static schedule. Our second algorithm BLCE removes the near G-optimal design step -- a dominant computational bottleneck in prior strictly batched static-grid methods -- yet preserves minimax-optimal regret and achieves the lowest known runtime complexity among optimal algorithms. We further extend these rare-update and computational principles to generalized linear contextual bandits. Overall, our results yield minimax-optimal algorithms for linear contextual bandits and a near-optimal generalized-linear extension under $O(\log\log T)$ parameter updates, while remaining computationally efficient in practice. Comments: Accepted at ICML 2026 Subjects: Machine Learning (stat.ML) ; Machine Learning (cs.LG) Cite as: arXiv:2606.00984 [stat.ML] (or arXiv:2606.00984v3 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2606.00984 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sanghoon Yu [ view email ] [v1] Sun, 31 May 2026 03:46:16 UTC (16,436 KB) [v2] Sat, 15 Aug 2026 23:44:16 UTC (16,438 KB) [v3] Sat, 22 Aug 2026 04:42:03 UTC (16,438 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2026-06 Change to browse by: cs cs.LG stat References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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