Dynamic Batch Learning in High-Dimensional Sparse Linear Contextual Bandits

Zhimei Ren () and Zhengyuan Zhou ()
Additional contact information
Zhimei Ren: Department of Statistics and Data Science, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Zhengyuan Zhou: Department of Technology, Operation and Statistics, Stern School of Business, New York University, New York, New York 10012

Management Science, 2024, vol. 70, issue 2, 1315-1342

Abstract: We study the problem of dynamic batch learning in high-dimensional sparse linear contextual bandits, where a decision maker, under a given maximum-number-of-batch constraint and only able to observe rewards at the end of each batch, can dynamically decide how many individuals to include in the next batch (at the end of the current batch) and what personalized action-selection scheme to adopt within each batch. Such batch constraints are ubiquitous in a variety of practical contexts, including personalized product offerings in marketing and medical treatment selection in clinical trials. We characterize the fundamental learning limit in this problem via a regret lower bound and provide a matching upper bound (up to log factors), thus prescribing an optimal scheme for this problem. To the best of our knowledge, our work provides the first inroad into a theoretical understanding of dynamic batch learning in high-dimensional sparse linear contextual bandits. Notably, even a special case of our result—when no batch constraint is present—yields that the simple exploration-free algorithm using the LASSO estimator already achieves the minimax optimal O ˜ ( s 0 T ) regret bound ( s 0 is the sparsity parameter or an upper bound thereof and T is the learning horizon) for standard online learning in high-dimensional linear contextual bandits (for the no-margin case), a result that appears unknown in the emerging literature of high-dimensional contextual bandits.

Keywords: dynamic batch learning; LASSO; high-dimensional statistics; contextual bandits; sparsity (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/mnsc.2023.4895 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:70:y:2024:i:2:p:1315-1342

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().