# Distribution-free Contextual Dynamic Pricing arXiv: https://arxiv.org/abs/2109.07340 ยท HTML: https://mlsanity.com/paper/2109.07340/ ## Key facts - Cited by 22 papers in the map (data through 14 Oct 2026). - Builds on 22 of its 59 references that are in the map. - First posted on arXiv 15 Sep 2021. ## Builds on (most cited first, 22 of 22) - [Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles](https://mlsanity.com/paper/2002.04926/) (2020) - [Learning with Good Feature Representations in Bandits and in RL with a Generative Model](https://mlsanity.com/paper/1911.07676/) (2019) - [Weighted Linear Bandits for Non-Stationary Environments](https://mlsanity.com/paper/1909.09146/) (2019) - [Adapting to Misspecification in Contextual Bandits](https://mlsanity.com/paper/2107.05745/) (2021) - [Model Selection in Contextual Stochastic Bandit Problems](https://mlsanity.com/paper/2003.01704/) (2020) - [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016) - [A Simple Approach for Non-stationary Linear Bandits](https://mlsanity.com/paper/2103.05324/) (2021) - [Hedging the Drift: Learning to Optimize under Non-Stationarity](https://mlsanity.com/paper/1903.01461/) (2019) - [Meta Dynamic Pricing: Transfer Learning Across Experiments](https://mlsanity.com/paper/1902.10918/) (2019) - [Online learning in repeated auctions](https://mlsanity.com/paper/1511.05720/) (2015) - [Dynamic Incentive-aware Learning: Robust Pricing in Contextual Auctions](https://mlsanity.com/paper/2002.11137/) (2020) - [Dynamic Pricing with Demand Covariates](https://mlsanity.com/paper/1604.07463/) (2016) - [Dynamic Pricing with Finitely Many Unknown Valuations](https://mlsanity.com/paper/1807.03288/) (2018) - [Policy Optimization Using Semi-parametric Models for Dynamic Pricing](https://mlsanity.com/paper/2109.06368/) (2021) - [Perishability of Data: Dynamic Pricing under Varying-Coefficient Models](https://mlsanity.com/paper/1701.03537/) (2017) - [Low-Rank Bandit Methods for High-Dimensional Dynamic Pricing](https://mlsanity.com/paper/1801.10242/) (2018) - [Semi-parametric dynamic contextual pricing](https://mlsanity.com/paper/1901.02045/) (2019) - [Fairness, Welfare, and Equity in Personalized Pricing](https://mlsanity.com/paper/2012.11066/) (2020) - [Incentive-aware Contextual Pricing with Non-parametric Market Noise](https://mlsanity.com/paper/1911.03508/) (2019) - [Multi-Product Dynamic Pricing in High-Dimensions with Heterogeneous Price Sensitivity](https://mlsanity.com/paper/1901.01030/) (2019) - [A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint](https://mlsanity.com/paper/1812.09234/) (2018) - [Uncertainty Quantification for Demand Prediction in Contextual Dynamic Pricing](https://mlsanity.com/paper/2003.07017/) (2020) ## Built on by (most cited first, 22 of 22) - [Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise](https://mlsanity.com/paper/2201.11341/) (2022) - [Improved Algorithms for Contextual Dynamic Pricing](https://mlsanity.com/paper/2406.11316/) (2024) - [Pricing with Contextual Elasticity and Heteroscedastic Valuation](https://mlsanity.com/paper/2312.15999/) (2023) - [Market Making without Regret](https://mlsanity.com/paper/2411.13993/) (2024) - [Regulatory Instruments for Fair Personalized Pricing](https://mlsanity.com/paper/2202.04245/) (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) - [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) - [Offline Deep Reinforcement Learning for Dynamic Pricing of Consumer Credit](https://mlsanity.com/paper/2203.03003/) (2022) - [Contextual Dynamic Pricing with Strategic Buyers](https://mlsanity.com/paper/2307.04055/) (2023) - [Insurance pricing on price comparison websites via reinforcement learning](https://mlsanity.com/paper/2308.06935/) (2023) - [Low-Rank Online Dynamic Assortment with Dual Contextual Information](https://mlsanity.com/paper/2404.17592/) (2024) - [Minimax Optimality in Contextual Dynamic Pricing with General Valuation Models](https://mlsanity.com/paper/2406.17184/) (2024) - [Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand](https://mlsanity.com/paper/2605.05609/) (2026) - [A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits](https://mlsanity.com/paper/2501.10722/) (2025) - [Learning to Sell a Focal-ancillary Combination](https://mlsanity.com/paper/2207.11545/) (2022) - [Parameter-Adaptive Dynamic Pricing](https://mlsanity.com/paper/2503.00929/) (2025) - [Contextual Learning for Stochastic Optimization](https://mlsanity.com/paper/2505.16829/) (2025) - [Contextual Dynamic Pricing with Heterogeneous Buyers](https://mlsanity.com/paper/2512.09513/) (2025) - [Nonparametric Learning and Earning with One-Point Feedback under Nonstationarity](https://mlsanity.com/paper/2605.21263/) (2026) - [Learning to Price and Stock Under Contextual and Censored Demand](https://mlsanity.com/paper/2609.06083/) (2026) ## Abstract (arXiv) Contextual dynamic pricing aims to set personalized prices based on sequential interactions with customers. At each time period, a customer who is interested in purchasing a product comes to the platform. The customer's valuation for the product is a linear function of contexts, including product and customer features, plus some random market noise. The seller does not observe the customer's true valuation, but instead needs to learn the valuation by leveraging contextual information and historical binary purchase feedbacks. Existing models typically assume full or partial knowledge of the random noise distribution. In this paper, we consider contextual dynamic pricing with unknown random noise in the valuation model. Our distribution-free pricing policy learns both the contextual function and the market noise simultaneously. A key ingredient of our method is a novel perturbed linear bandit framework, where a modified linear upper confidence bound algorithm is proposed to balance the exploration of market noise and the exploitation of the current knowledge for better pricing. We establish the regret upper bound and a matching lower bound of our policy in the perturbed linear bandit framework and prove a sub-linear regret bound in the considered pricing problem. Finally, we demonstrate the superior performance of our policy on simulations and a real-life auto-loan dataset.