# Dynamic Pricing in High-dimensions

arXiv: https://arxiv.org/abs/1609.07574 · HTML: https://mlsanity.com/paper/1609.07574/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2016.

## Built on by (most cited first, 30 of 55)

- [Policy Optimization Using Semi-parametric Models for Dynamic Pricing](https://mlsanity.com/paper/2109.06368/) (2021)
- [Logarithmic Regret in Feature-based Dynamic Pricing](https://mlsanity.com/paper/2102.10221/) (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)
- [Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise](https://mlsanity.com/paper/2201.11341/) (2022)
- [Dynamic pricing and assortment under a contextual MNL demand](https://mlsanity.com/paper/2110.10018/) (2021)
- [Learning to Bid in Contextual First Price Auctions](https://mlsanity.com/paper/2109.03173/) (2021)
- [Differential Privacy in Personalized Pricing with Nonparametric Demand Models](https://mlsanity.com/paper/2109.04615/) (2021)
- [Incentivized Learning in Principal-Agent Bandit Games](https://mlsanity.com/paper/2403.03811/) (2024)
- [Improved Algorithms for Contextual Dynamic Pricing](https://mlsanity.com/paper/2406.11316/) (2024)
- [On Dynamic Pricing with Covariates](https://mlsanity.com/paper/2112.13254/) (2021)
- [Doubly Fair Dynamic Pricing](https://mlsanity.com/paper/2209.11837/) (2022)
- [Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricing](https://mlsanity.com/paper/2309.08634/) (2023)
- [Fairness-aware Online Price Discrimination with Nonparametric Demand Models](https://mlsanity.com/paper/2111.08221/) (2021)
- [Stateful Offline Contextual Policy Evaluation and Learning](https://mlsanity.com/paper/2110.10081/) (2021)
- [Loss Functions for Discrete Contextual Pricing with Observational Data](https://mlsanity.com/paper/2111.09933/) (2021)
- [Learning to Price Against a Moving Target](https://mlsanity.com/paper/2106.04689/) (2021)
- [Pricing with Contextual Elasticity and Heteroscedastic Valuation](https://mlsanity.com/paper/2312.15999/) (2023)
- [Regulatory Instruments for Fair Personalized Pricing](https://mlsanity.com/paper/2202.04245/) (2022)
- [Density-Based Algorithms for Corruption-Robust Contextual Search and Convex Optimization](https://mlsanity.com/paper/2206.07528/) (2022)
- [Utility Fairness in Contextual Dynamic Pricing with Demand Learning](https://mlsanity.com/paper/2311.16528/) (2023)
- [A Parametric Contextual Online Learning Theory of Brokerage](https://mlsanity.com/paper/2407.01566/) (2024)
- [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)
- [Dynamic Pricing with Adversarially-Censored Demands](https://mlsanity.com/paper/2502.06168/) (2025)
- [Contextual Dynamic Pricing with Strategic Buyers](https://mlsanity.com/paper/2307.04055/) (2023)
- [Learning to Price with Resource Constraints: From Full Information to Machine-Learned Prices](https://mlsanity.com/paper/2501.14155/) (2025)
- [Contextual Online Bilateral Trade](https://mlsanity.com/paper/2602.12903/) (2026)
- [Minimax Optimality in Contextual Dynamic Pricing with General Valuation Models](https://mlsanity.com/paper/2406.17184/) (2024)
- [Learning to Price Homogeneous Data](https://mlsanity.com/paper/2407.05484/) (2024)

## Abstract (arXiv)

We study the pricing problem faced by a firm that sells a large number of products, described via a wide range of features, to customers that arrive over time. Customers independently make purchasing decisions according to a general choice model that includes products features and customers' characteristics, encoded as d-dimensional numerical vectors, as well as the price offered. The parameters of the choice model are a priori unknown to the firm, but can be learned as the (binary-valued) sales data accrues over time. The firm's objective is to minimize the regret, i.e., the expected revenue loss against a clairvoyant policy that knows the parameters of the choice model in advance, and always offers the revenue-maximizing price. This setting is motivated in part by the prevalence of online marketplaces that allow for real-time pricing. We assume a structured choice model, parameters of which depend on s0 out of the d product features. We propose a dynamic policy, called Regularized Maximum Likelihood Pricing (RMLP) that leverages the (sparsity) structure of the high-dimensional model and obtains a logarithmic regret in T. More specifically, the regret of our algorithm is of O(s0 log d · log T). Furthermore, we show that no policy can obtain regret better than O(s0 (log d + log T)).