Low-Rank Online Dynamic Assortment with Dual Contextual Information

TL;DR

This paper introduces a low-rank model for real-time personalized assortment optimization considering user and item features, with an efficient algorithm and theoretical regret bounds, validated through simulations and real data.

Contribution

It proposes a novel low-rank dynamic assortment model and an efficient estimation algorithm with theoretical guarantees, addressing high-dimensional challenges in online recommendations.

Findings

Regret bound of ~O((d_1+d_2)rT) established

Algorithm effectively estimates intrinsic subspaces in high dimensions

Method outperforms prior approaches in simulations and real dataset

Abstract

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.