# Low-Rank Online Dynamic Assortment with Dual Contextual Information

arXiv: https://arxiv.org/abs/2404.17592 · HTML: https://mlsanity.com/paper/2404.17592/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 55 references that are in the map.
- First posted on arXiv 19 Apr 2024.

## Builds on (most cited first, 21 of 21)

- [Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview](https://mlsanity.com/paper/1809.09573/) (2018)
- [Bilinear Bandits with Low-rank Structure](https://mlsanity.com/paper/1901.02470/) (2019)
- [MNL-Bandit: A Dynamic Learning Approach to Assortment Selection](https://mlsanity.com/paper/1706.03880/) (2017)
- [Doubly-Robust Lasso Bandit](https://mlsanity.com/paper/1907.11362/) (2019)
- [Convergence Analysis for Rectangular Matrix Completion Using Burer-Monteiro Factorization and Gradient Descent](https://mlsanity.com/paper/1605.07051/) (2016)
- [Thompson Sampling for the MNL-Bandit](https://mlsanity.com/paper/1706.00977/) (2017)
- [Stochastic Low-Rank Bandits](https://mlsanity.com/paper/1712.04644/) (2017)
- [Dynamic Assortment Optimization with Changing Contextual Information](https://mlsanity.com/paper/1810.13069/) (2018)
- [Estimating Optimal Infinite Horizon Dynamic Treatment Regimes via pT-Learning](https://mlsanity.com/paper/2110.10719/) (2021)
- [Distribution-free Contextual Dynamic Pricing](https://mlsanity.com/paper/2109.07340/) (2021)
- [Multinomial Logit Contextual Bandits: Provable Optimality and Practicality](https://mlsanity.com/paper/2103.13929/) (2021)
- [Dynamic pricing and assortment under a contextual MNL demand](https://mlsanity.com/paper/2110.10018/) (2021)
- [Efficient Frameworks for Generalized Low-Rank Matrix Bandit Problems](https://mlsanity.com/paper/2401.07298/) (2024)
- [Statistical Inferences of Linear Forms for Noisy Matrix Completion](https://mlsanity.com/paper/1909.00116/) (2019)
- [Dynamic Assortment Personalization in High Dimensions](https://mlsanity.com/paper/1610.05604/) (2016)
- [Tuning parameter selection in high dimensional penalized likelihood](https://mlsanity.com/paper/1605.03321/) (2016)
- [Inference for Low-rank Tensors -- No Need to Debias](https://mlsanity.com/paper/2012.14844/) (2020)
- [Stochastic Low-rank Tensor Bandits for Multi-dimensional Online Decision Making](https://mlsanity.com/paper/2007.15788/) (2020)
- [Robust Dynamic Assortment Optimization in the Presence of Outlier Customers](https://mlsanity.com/paper/1910.04183/) (2019)
- [Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricing](https://mlsanity.com/paper/2309.08634/) (2023)
- [Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Information](https://mlsanity.com/paper/2403.14899/) (2024)

## Built on by (most cited first, 2 of 2)

- [Generalized Low-Rank Matrix Contextual Bandits with Graph Information](https://mlsanity.com/paper/2507.17528/) (2025)
- [Privacy-Preserving Dynamic Assortment Selection](https://mlsanity.com/paper/2410.22488/) (2024)

## Abstract (arXiv)

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 tildeO((d1+d2)r√T), where d1, d2 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.