# A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint

arXiv: https://arxiv.org/abs/1812.09234 · HTML: https://mlsanity.com/paper/1812.09234/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2018.

## Built on by (most cited first, 9 of 9)

- [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)
- [Federated X-Armed Bandit](https://mlsanity.com/paper/2205.15268/) (2022)
- [Online Pricing and Allocation with Demand Learning and Fulfillment Cost](https://mlsanity.com/paper/2501.18049/) (2025)
- [Collaborative Intelligence in Sequential Experiments: A Human-in-the-Loop Framework for Drug Discovery](https://mlsanity.com/paper/2405.03942/) (2024)
- [Smoothness-Adaptive Dynamic Pricing with Nonparametric Demand Learning](https://mlsanity.com/paper/2310.07558/) (2023)
- [Parameter-Adaptive Dynamic Pricing](https://mlsanity.com/paper/2503.00929/) (2025)
- [Resource-Adaptive Primal-Dual Learning for One-Warehouse Multi-Store Systems with Censored Demand](https://mlsanity.com/paper/2608.14096/) (2026)
- [Nonparametric Contextual Pricing and Inventory Learning under Censored Demand](https://mlsanity.com/paper/2608.30944/) (2026)

## Abstract (arXiv)

We consider the problem of a firm seeking to use personalized pricing to sell an exogenously given stock of a product over a finite selling horizon to different consumer types. We assume that the type of an arriving consumer can be observed but the demand function associated with each type is initially unknown. The firm sets personalized prices dynamically for each type and attempts to maximize the revenue over the season. We provide a learning algorithm that is near-optimal when the demand and capacity scale in proportion. The algorithm utilizes the primal-dual formulation of the problem and learns the dual optimal solution explicitly. It allows the algorithm to overcome the curse of dimensionality (the rate of regret is independent of the number of types) and sheds light on novel algorithmic designs for learning problems with resource constraints.