Low-Rank Online Dynamic Assortment with Dual Contextual Information

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 paper, 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 utilizes the upper confidence bound approach to address the exploration-exploitation trade-off in online decision making. Theoretically, we establish a regret bound of O˜((d1+d2)rT), where d1,d2 represent the dimensions of the user and item features respectively, <i>r</i> is the rank of the parameter matrix, and <i>T</i> 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.

随着电子商务的蓬勃发展，从海量商品目录中实时提供个性化推荐，已成为零售平台面临的关键挑战。实现营收最大化需综合考量个体顾客特征与可用商品属性，以随时间持续优化商品组合。本文针对兼具用户与商品双重上下文的动态商品组合问题展开研究。在高维场景下，特征维度的二次增长会大幅增加计算与估计的复杂度。为解决这一难题，我们提出一种新型低秩动态商品组合模型，将该问题转化为可高效处理的规模。随后我们设计了一种高效算法，可估计本征子空间，并结合上置信界（upper confidence bound, UCB）方法处理在线决策中的探索-利用权衡问题。理论层面，我们推导得到累计遗憾界为Õ((d₁+d₂)rT)，其中d₁、d₂分别代表用户特征与商品特征的维度，r为参数矩阵的秩，T为时间跨度。相较于现有研究，该界借助低秩结构实现了显著的性能提升。大量仿真实验以及在Expedia酒店推荐数据集上的应用，进一步验证了所提方法的优越性。