# Smoothness-Adaptive Dynamic Pricing with Nonparametric Demand Learning

arXiv: https://arxiv.org/abs/2310.07558 · HTML: https://mlsanity.com/paper/2310.07558/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 44 references that are in the map.
- First posted on arXiv 11 Oct 2023.

## Builds on (most cited first, 10 of 10)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [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)
- [Logarithmic Regret in Feature-based Dynamic Pricing](https://mlsanity.com/paper/2102.10221/) (2021)
- [Perishability of Data: Dynamic Pricing under Varying-Coefficient Models](https://mlsanity.com/paper/1701.03537/) (2017)
- [Smoothness-Adaptive Contextual Bandits](https://mlsanity.com/paper/1910.09714/) (2019)
- [Smooth Bandit Optimization: Generalization to H"older Space](https://mlsanity.com/paper/2012.06076/) (2020)
- [A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint](https://mlsanity.com/paper/1812.09234/) (2018)
- [Polynomial Cost of Adaptation for X -Armed Bandits](https://mlsanity.com/paper/1905.10221/) (2019)

## Built on by (most cited first, 1 of 1)

- [Parameter-Adaptive Dynamic Pricing](https://mlsanity.com/paper/2503.00929/) (2025)

## Abstract (arXiv)

We study the dynamic pricing problem where the demand function is nonparametric and H"older smooth, and we focus on adaptivity to the unknown H"older smoothness parameter β of the demand function. Traditionally the optimal dynamic pricing algorithm heavily relies on the knowledge of β to achieve a minimax optimal regret of widetildeO(T^fracβ+12β+1). However, we highlight the challenge of adaptivity in this dynamic pricing problem by proving that no pricing policy can adaptively achieve this minimax optimal regret without knowledge of β. Motivated by the impossibility result, we propose a self-similarity condition to enable adaptivity. Importantly, we show that the self-similarity condition does not compromise the problem's inherent complexity since it preserves the regret lower bound Omega(T^fracβ+12β+1). Furthermore, we develop a smoothness-adaptive dynamic pricing algorithm and theoretically prove that the algorithm achieves this minimax optimal regret bound without the prior knowledge β.