# Policy Optimization Using Semi-parametric Models for Dynamic Pricing

arXiv: https://arxiv.org/abs/2109.06368 · HTML: https://mlsanity.com/paper/2109.06368/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 84 references that are in the map.
- First posted on arXiv 13 Sep 2021.

## 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 Demand Covariates](https://mlsanity.com/paper/1604.07463/) (2016)
- [Contextual Search via Intrinsic Volumes](https://mlsanity.com/paper/1804.03195/) (2018)
- [Dynamic Pricing with Finitely Many Unknown Valuations](https://mlsanity.com/paper/1807.03288/) (2018)
- [Privacy-Preserving Dynamic Personalized Pricing with Demand Learning](https://mlsanity.com/paper/2009.12920/) (2020)
- [Perishability of Data: Dynamic Pricing under Varying-Coefficient Models](https://mlsanity.com/paper/1701.03537/) (2017)
- [Semi-parametric dynamic contextual pricing](https://mlsanity.com/paper/1901.02045/) (2019)
- [Context-Based Dynamic Pricing with Online Clustering](https://mlsanity.com/paper/1902.06199/) (2019)
- [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)
- [Uncertainty Quantification for Demand Prediction in Contextual Dynamic Pricing](https://mlsanity.com/paper/2003.07017/) (2020)

## Built on by (most cited first, 23 of 23)

- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [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)
- [Improved Algorithms for Contextual Dynamic Pricing](https://mlsanity.com/paper/2406.11316/) (2024)
- [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)
- [Pricing with Contextual Elasticity and Heteroscedastic Valuation](https://mlsanity.com/paper/2312.15999/) (2023)
- [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)
- [Contextual Dynamic Pricing with Strategic Buyers](https://mlsanity.com/paper/2307.04055/) (2023)
- [Minimax Optimality in Contextual Dynamic Pricing with General Valuation Models](https://mlsanity.com/paper/2406.17184/) (2024)
- [Dynamic Assortment Selection and Pricing with Censored Preference Feedback](https://mlsanity.com/paper/2504.02324/) (2025)
- [Transfer Faster, Price Smarter: Minimax Dynamic Pricing under Cross-Market Preference Shift](https://mlsanity.com/paper/2505.17203/) (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)
- [Smoothness-Adaptive Dynamic Pricing with Nonparametric Demand Learning](https://mlsanity.com/paper/2310.07558/) (2023)
- [Revenue Maximization Under Sequential Price Competition Via The Estimation Of s-Concave Demand Functions](https://mlsanity.com/paper/2503.16737/) (2025)
- [Parameter-Adaptive Dynamic Pricing](https://mlsanity.com/paper/2503.00929/) (2025)
- [Contextual Dynamic Pricing with Heterogeneous Buyers](https://mlsanity.com/paper/2512.09513/) (2025)
- [Do Not Trust The Auctioneer: Learning to Bid in Feedback-Manipulated Auctions](https://mlsanity.com/paper/2605.22438/) (2026)
- [Learning to Price and Stock Under Contextual and Censored Demand](https://mlsanity.com/paper/2609.06083/) (2026)

## Abstract (arXiv)

In this paper, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of a sale is observed. Our model setting is similar to Javanmard and Nazerzadeh [2019] except that we expand the demand curve to a semiparametric model and need to learn dynamically both parametric and nonparametric components. We propose a dynamic statistical learning and decision-making policy that combines semiparametric estimation from a generalized linear model with an unknown link and online decision-making to minimize regret (maximize revenue). Under mild conditions, we show that for a market noise c.d.f. F(·) with m-th order derivative (m≥ 2), our policy achieves a regret upper bound of tildeOd(T^frac2m+14m-1), where T is time horizon and tildeOd is the order that hides logarithmic terms and the dimensionality of feature d. The upper bound is further reduced to tildeOd(√T) if F is super smooth whose Fourier transform decays exponentially. In terms of dependence on the horizon T, these upper bounds are close to Omega(√T), the lower bound where F belongs to a parametric class. We further generalize these results to the case with dynamically dependent product features under the strong mixing condition.