Low-Rank Online Dynamic Assortment with Dual Contextual Information

• 成果类型: Article; Early Access
• 署名作者: Lee, Seong Jin; Sun, Will Wei; Liu, Yufeng
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; Purdue University System; Purdue University; University of Michigan System; University of Michigan
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2025.2597043
• 发表日期: 2026-03-05
• 关键词: Bandit algorithm; Low-rankness; online decision making; Regret Analysis; Reinforcement Learning; Matrix Factorization; optimization; selection; MODEL

摘要

As e-commerce expands, delivering real-time personalized recommendations from vast catalogs poses a critical challenge for retail platforms. Maximizing revenue requires careful consideration of both individual customer characteristics and available item features to continuously optimize assortments over time. In this article, we consider the dynamic assortment problem with dual contexts-user and item features. In high-dimensional scenarios, the quadratic growth of dimensions complicates computation and estimation. To tackle this challenge, we introduce a new low-rank dynamic assortment model to transform this problem into a manageable scale. Then we propose an efficient algorithm that estimates the intrinsic subspaces and uses the upper confidence bound approach to address the exploration-exploitation tradeoff in online decision making. Theoretically, we establish a regret bound of O((d(1)+d(2))rT), where d(1),d(2) represent the dimensions of the user and item features, respectively, r is the rank of the parameter matrix, and T denotes the time horizon. This bound represents a substantial improvement over prior literature, achieved by leveraging the low-rank structure. Extensive simulations and an application to the Expedia hotel recommendation dataset further demonstrate the advantages of our proposed method. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.