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 $\tilde{O}((d_1+d_2)r\sqrt{T})$, 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.

翻译：随着电子商务的扩展，从海量商品目录中提供实时个性化推荐成为零售平台面临的关键挑战。最大化收入需要仔细考虑个体顾客特征与可用商品属性，以持续优化随时间变化的商品搭配。本文研究了具有双重上下文——用户特征与商品特征——的动态商品搭配问题。在高维场景下，维度的二次增长使得计算与估计变得复杂。为应对这一挑战，我们引入了一种新的低秩动态商品搭配模型，将问题转化为可管理的规模。随后，我们提出了一种高效算法，该算法估计内在子空间并利用上置信界方法处理在线决策中的探索-利用权衡。理论上，我们建立了$\tilde{O}((d_1+d_2)r\sqrt{T})$的遗憾界，其中$d_1, d_2$分别表示用户与商品特征的维度，$r$为参数矩阵的秩，$T$表示时间范围。通过利用低秩结构，该界限相较于先前文献取得了显著改进。大量仿真实验以及在Expedia酒店推荐数据集上的应用进一步证明了我们所提方法的优势。