# Dynamic Pricing in the Linear Valuation Model using Shape Constraints

arXiv: https://arxiv.org/abs/2502.05776 · HTML: https://mlsanity.com/paper/2502.05776/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 9 Feb 2025.

## Builds on (most cited first, 12 of 12)

- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [Dynamic Incentive-aware Learning: Robust Pricing in Contextual Auctions](https://mlsanity.com/paper/2002.11137/) (2020)
- [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)
- [Distribution-free Contextual Dynamic Pricing](https://mlsanity.com/paper/2109.07340/) (2021)
- [Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise](https://mlsanity.com/paper/2201.11341/) (2022)
- [Context-Based Dynamic Pricing with Online Clustering](https://mlsanity.com/paper/1902.06199/) (2019)
- [Multi-Product Dynamic Pricing in High-Dimensions with Heterogeneous Price Sensitivity](https://mlsanity.com/paper/1901.01030/) (2019)
- [Improved Algorithms for Contextual Dynamic Pricing](https://mlsanity.com/paper/2406.11316/) (2024)
- [Monotone Least Squares and Isotonic Quantiles](https://mlsanity.com/paper/1901.02398/) (2019)
- [Learning the Distribution Map in Reverse Causal Performative Prediction](https://mlsanity.com/paper/2405.15172/) (2024)
- [Multi-Task Dynamic Pricing in Credit Market with Contextual Information](https://mlsanity.com/paper/2410.14839/) (2024)

## Built on by (most cited first, 4 of 4)

- [Pre-Trained AI Model Assisted Online Decision-Making under Missing Covariates: A Theoretical Perspective](https://mlsanity.com/paper/2507.07852/) (2025)
- [Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand](https://mlsanity.com/paper/2605.05609/) (2026)
- [Revenue Maximization Under Sequential Price Competition Via The Estimation Of s-Concave Demand Functions](https://mlsanity.com/paper/2503.16737/) (2025)
- [Harnessing Unimodality in Semiparametric Contextual Pricing via Oracle Price Map Learning](https://mlsanity.com/paper/2605.15411/) (2026)

## Abstract (arXiv)

We propose a shape-constrained approach to dynamic pricing for censored data in the linear valuation model eliminating the need for tuning parameters commonly required by existing methods. Previous works have addressed the challenge of unknown market noise distribution F0 using strategies ranging from kernel methods to reinforcement learning algorithms, such as bandit techniques and upper confidence bounds (UCB), under the assumption that F0 satisfies Lipschitz (or stronger) conditions. In contrast, our method relies on isotonic regression under the weaker assumption that F0 is α-H"older continuous for some α ∈ (0,1], for which we derive a regret upper bound. Simulations and experiments with real-world data obtained by Welltower Inc (a major healthcare Real Estate Investment Trust) consistently demonstrate that our method attains lower empirical regret in comparison to several existing methods in the literature while offering the advantage of being tuning-parameter free.