# Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricing

arXiv: https://arxiv.org/abs/2309.08634 · HTML: https://mlsanity.com/paper/2309.08634/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 94 references that are in the map.
- First posted on arXiv 14 Sep 2023.

## Builds on (most cited first, 30 of 33)

- [Neural Contextual Bandits with Deep Representation and Shallow Exploration](https://mlsanity.com/paper/2012.01780/) (2020)
- [Bandits and Experts in Metric Spaces](https://mlsanity.com/paper/1312.1277/) (2013)
- [High-Dimensional Sparse Linear Bandits](https://mlsanity.com/paper/2011.04020/) (2020)
- [Generalized Low Rank Models](https://mlsanity.com/paper/1410.0342/) (2014)
- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [Bilinear Bandits with Low-rank Structure](https://mlsanity.com/paper/1901.02470/) (2019)
- [Impact of Representation Learning in Linear Bandits](https://mlsanity.com/paper/2010.06531/) (2020)
- [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)
- [Low-Rank Generalized Linear Bandit Problems](https://mlsanity.com/paper/2006.02948/) (2020)
- [Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics](https://mlsanity.com/paper/1605.00353/) (2016)
- [Near-optimal Representation Learning for Linear Bandits and Linear RL](https://mlsanity.com/paper/2102.04132/) (2021)
- [EE-Net: Exploitation-Exploration Neural Networks in Contextual Bandits](https://mlsanity.com/paper/2110.03177/) (2021)
- [Contextual Bandits with Continuous Actions: Smoothing, Zooming, and Adapting](https://mlsanity.com/paper/1902.01520/) (2019)
- [Meta Dynamic Pricing: Transfer Learning Across Experiments](https://mlsanity.com/paper/1902.10918/) (2019)
- [Dynamic Pricing with Demand Covariates](https://mlsanity.com/paper/1604.07463/) (2016)
- [Leveraging Good Representations in Linear Contextual Bandits](https://mlsanity.com/paper/2104.03781/) (2021)
- [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)
- [Policy Optimization Using Semi-parametric Models for Dynamic Pricing](https://mlsanity.com/paper/2109.06368/) (2021)
- [Vintage Factor Analysis with Varimax Performs Statistical Inference](https://mlsanity.com/paper/2004.05387/) (2020)
- [Stochastic Linear Bandits with Hidden Low Rank Structure](https://mlsanity.com/paper/1901.09490/) (2019)
- [Dynamic Assortment Personalization in High Dimensions](https://mlsanity.com/paper/1610.05604/) (2016)
- [Context-Based Dynamic Pricing with Online Clustering](https://mlsanity.com/paper/1902.06199/) (2019)
- [Nearly Dimension-Independent Sparse Linear Bandit over Small Action Spaces via Best Subset Selection](https://mlsanity.com/paper/2009.02003/) (2020)
- [Random Forest for the Contextual Bandit Problem - extended version](https://mlsanity.com/paper/1504.06952/) (2015)
- [Robust Dynamic Assortment Optimization in the Presence of Outlier Customers](https://mlsanity.com/paper/1910.04183/) (2019)
- [A Note on a Tight Lower Bound for MNL-Bandit Assortment Selection Models](https://mlsanity.com/paper/1709.06109/) (2017)
- [Embracing the Blessing of Dimensionality in Factor Models](https://mlsanity.com/paper/1610.07697/) (2016)
- [Best Arm Identification in Graphical Bilinear Bandits](https://mlsanity.com/paper/2012.07641/) (2020)

## Built on by (most cited first, 8 of 8)

- [Incentivized Learning in Principal-Agent Bandit Games](https://mlsanity.com/paper/2403.03811/) (2024)
- [Low-Rank Contextual Reinforcement Learning from Heterogeneous Human Feedback](https://mlsanity.com/paper/2412.19436/) (2024)
- [Low-Rank Bandits via Tight Two-to-Infinity Singular Subspace Recovery](https://mlsanity.com/paper/2402.15739/) (2024)
- [Generalized Low-Rank Matrix Contextual Bandits with Graph Information](https://mlsanity.com/paper/2507.17528/) (2025)
- [Low-Rank Online Dynamic Assortment with Dual Contextual Information](https://mlsanity.com/paper/2404.17592/) (2024)
- [A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits](https://mlsanity.com/paper/2501.10722/) (2025)
- [Navigating Sparsities in High-Dimensional Linear Contextual Bandits](https://mlsanity.com/paper/2510.08435/) (2025)
- [CAROL: Context-Aware Online Learning for Fuzzer Scheduling](https://mlsanity.com/paper/2609.06772/) (2026)

## Abstract (arXiv)

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.