Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricing

• 成果类型: Article; Early Access
• 署名作者: Cai, Junhui; Chen, Ran; Wainwright, Martin J.; Zhao, Linda
• 署名单位: University of Notre Dame; Washington University (WUSTL); Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of Pennsylvania
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2024.08311
• 发表日期: 2026
• 关键词: contextual bandits; on-line decision-making; -dimensional statistics; low-rank matrices; factor models

摘要

Key challenges in running a business include deciding which products or services to present to consumers (the assortment problem) and how to price products (the pricing problem) to maximize revenue or profit. Instead of considering these problems isolation, we address assortment-pricing jointly and tackle the intrinsic doubly high dimensionality-both actions and contextual vectors can take continuous value in high dimensional spaces. We propose a doubly high-dimensional contextual bandit model formulate this problem. To circumvent the curse of dimensionality, our model is simple, yet flexible, capturing the interaction effects between covariates (context) and actions on the reward via a low-rank representation matrix. The resulting class of models is reasonably expressive while remaining interpretable through latent factors and includes various bandit and pricing models as special cases, making it suitable for applications involving simultaneous multiple decision-making beyond joint assortment-pricing. We develop computationally tractable procedure that combines an exploration/exploitation protocol with an efficient low-rank matrix estimator. We provide a nonasymptotic instance dependent regret bound involving dimensions and rank in addition to the time horizon. Simulations on standard bandit and pricing models-special cases of our model- demonstrate that our method yields lower regret than state-of-the-art methods. Real-world assortment-pricing case studies, from an industry-leading instant noodle manufacturer an emerging beauty start-up, underscore the gains achievable using our method, showing at least three-fold gains in revenue/profit and the interpretability of the latent factor models that are learned.