Sequential Batch Learning in Finite-Action Linear Contextual Bandits

[2004.06321] Sequential Batch Learning in Finite-Action Linear Contextual Bandits Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2004.06321 (cs) [Submitted on 14 Apr 2020 ( v1 ), last revised 16 Aug 2026 (this version, v2)] Title: Sequential Batch Learning in Finite-Action Linear Contextual Bandits Authors: Yanjun Han , Zhengqing Zhou , Zihao Hu , Jose Blanchet , Peter W. Glynn , Yinyu Ye , Zhengyuan Zhou View a PDF of the paper titled Sequential Batch Learning in Finite-Action Linear Contextual Bandits, by Yanjun Han and 6 other authors View PDF HTML (experimental) Abstract: We study the sequential batch learning problem in linear contextual bandits with finite action sets, where the decision maker is constrained to split incoming individuals into (at most) a fixed number of batches and can only observe outcomes for the individuals within a batch at the batch's end. Compared with both standard online contextual-bandit learning and offline policy learning in contextual bandits, this sequential batch learning problem provides a finer-grained formulation of many personalized sequential decision making problems in practical applications, including medical treatment in clinical trials, product recommendation in e-commerce and adaptive experiment design in crowdsourcing. We study two settings of the problem: one where the contexts are arbitrarily generated and the other where the context vectors are mutually independent across actions and time and follow a common Gaussian distribution. In each setting, we establish a regret lower bound and provide an algorithm, whose regret upper bound nearly matches the lower bound. As an important insight revealed therefrom, in the former setting, we show that the number of batches required to achieve the fully online performance is polynomial in the time horizon, while for the latter setting, a pure-exploitation algorithm with a judicious batch partition scheme achieves the fully online performance even when the number of batches is less than logarithmic in the time horizon. In the stochastic context setting, we additionally provide tight margin-based (i.e. instance-dependent) upper and lower regret bounds that delineate performance in terms of how difficult the problem instance is. Together, our results provide a near-complete characterization of sequential decision making in linear contextual bandits when batch constraints are present. Comments: To appear in Operations Research Subjects: Machine Learning (cs.LG) ; Information Theory (cs.IT); Machine Learning (stat.ML) Cite as: arXiv:2004.06321 [cs.LG] (or arXiv:2004.06321v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2004.06321 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yanjun Han [ view email ] [v1] Tue, 14 Apr 2020 06:47:40 UTC (40 KB) [v2] Sun, 16 Aug 2026 04:44:14 UTC (489 KB) Full-text links: Access Paper: View a PDF of the paper titled Sequential Batch Learning in Finite-Action Linear Contextual Bandits, by Yanjun Han and 6 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2020-04 Change to browse by: cs cs.IT math math.IT stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar DBLP - CS Bibliography listing | bibtex Yanjun Han Zhengqing Zhou Zhengyuan Zhou Jose H. Blanchet Peter W. 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