# Multi-Product Dynamic Pricing in High-Dimensions with Heterogeneous Price Sensitivity

arXiv: https://arxiv.org/abs/1901.01030 · HTML: https://mlsanity.com/paper/1901.01030/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2019.

## Built on by (most cited first, 12 of 12)

- [Policy Optimization Using Semi-parametric Models for Dynamic Pricing](https://mlsanity.com/paper/2109.06368/) (2021)
- [Distribution-free Contextual Dynamic Pricing](https://mlsanity.com/paper/2109.07340/) (2021)
- [Dynamic pricing and assortment under a contextual MNL demand](https://mlsanity.com/paper/2110.10018/) (2021)
- [Online Pricing and Allocation with Demand Learning and Fulfillment Cost](https://mlsanity.com/paper/2501.18049/) (2025)
- [Dynamic Pricing in the Linear Valuation Model using Shape Constraints](https://mlsanity.com/paper/2502.05776/) (2025)
- [Deep Learning for Choice Modeling](https://mlsanity.com/paper/2208.09325/) (2022)
- [Dynamic Assortment Selection and Pricing with Censored Preference Feedback](https://mlsanity.com/paper/2504.02324/) (2025)
- [Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand](https://mlsanity.com/paper/2605.05609/) (2026)
- [A Reinforcement Learning Approach in Multi-Phase Second-Price Auction Design](https://mlsanity.com/paper/2210.10278/) (2022)
- [DeepRule: An Integrated Framework for Automated Business Rule Generation via Deep Predictive Modeling and Hybrid Search Optimization](https://mlsanity.com/paper/2512.03607/) (2025)
- [Online Dynamic Pricing of Complementary Products](https://mlsanity.com/paper/2511.22291/) (2025)
- [Learning Choice Model Trees for Feature-Based Multi-Product Pricing: Exact Optimization and Field Evidence](https://mlsanity.com/paper/2609.16952/) (2026)

## Abstract (arXiv)

We consider the problem of multi-product dynamic pricing, in a contextual setting, for a seller of differentiated products. In this environment, the customers arrive over time and products are described by high-dimensional feature vectors. Each customer chooses a product according to the widely used Multinomial Logit (MNL) choice model and her utility depends on the product features as well as the prices offered. The seller a-priori does not know the parameters of the choice model but can learn them through interactions with customers. The seller's goal is to design a pricing policy that maximizes her cumulative revenue. This model is motivated by online marketplaces such as Airbnb platform and online advertising. We measure the performance of a pricing policy in terms of regret, which is the expected revenue loss with respect to a clairvoyant policy that knows the parameters of the choice model in advance and always sets the revenue-maximizing prices. We propose a pricing policy, named M3P, that achieves a T-period regret of O(log(Td) ( √T+ dlog(T))) under heterogeneous price sensitivity for products with features of dimension d. We also use tools from information theory to prove that no policy can achieve worst-case T-regret better than Omega(√T).