Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricing
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双重高维情境老虎机：用于产品组合与定价联合决策的可解释模型
- 研究问题
- 当消费者特征和可选行动都处于高维空间时，如何联合选择产品组合与价格，在控制学习成本的同时提高收入或利润？
- 方法与思路
- 作者用近似低秩矩阵刻画特征与行动的交互，以潜在因子提供解释，并结合探索利用机制和高效低秩矩阵估计。
- 材料陈述的贡献
- 摘要称方法具有遗憾界，模拟中遗憾低于所比较方法；两个企业案例报告收入或利润至少三倍提升，并展示潜在因子解释。
- 阅读关注点
- 应核对低秩与反馈机制的具体条件、遗憾界的维度依赖，以及企业案例的比较基准、实施方式和收益统计口径。
- 阅读边界
- 这是 arXiv 预印本，同行评审与接收未核实。摘要未说明案例收益的因果识别设计，不能将报告的提升外推为普遍效果。
原文摘要
Key challenges in running a retail business include how to select products 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 in isolation, we propose a joint approach to assortment-pricing based on contextual bandits. Our model is doubly high-dimensional, in that both context vectors and actions are allowed to take values in high-dimensional spaces. In order to circumvent the curse of dimensionality, we propose a simple yet flexible model that captures the interactions between covariates and actions via a (near) low-rank representation matrix. The resulting class of models is reasonably expressive while remaining interpretable through latent factors, and includes various structured linear bandit and pricing models as particular cases. We propose a computationally tractable procedure that combines an exploration/exploitation protocol with an efficient low-rank matrix estimator, and we prove bounds on its regret. Simulation results show that this method has lower regret than state-of-the-art methods applied to various standard bandit and pricing models. Real-world case studies on the assortment-pricing problem, from an industry-leading instant noodles company to an emerging beauty start-up, underscore the gains achievable using our method. In each case, we show at least three-fold gains in revenue or profit by our bandit method, as well as the interpretability of the latent factor models that are learned.