Smoothness-Adaptive Dynamic Pricing with Nonparametric Demand Learning

Zeqi Ye, Hansheng Jiang
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:1675-1683, 2024.

Abstract

We study the dynamic pricing problem where the demand function is nonparametric and Hölder smooth, and we focus on adaptivity to the unknown Hölder smoothness parameter $\beta$ of the demand function. Traditionally the optimal dynamic pricing algorithm heavily relies on the knowledge of $\beta$ to achieve a minimax optimal regret of $\widetilde{O}(T^{\frac{\beta+1}{2\beta+1}})$. 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 $\beta$. 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 $\Omega(T^{\frac{\beta+1}{2\beta+1}})$. 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 $\beta$.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-ye24b, title = { Smoothness-Adaptive Dynamic Pricing with Nonparametric Demand Learning }, author = {Ye, Zeqi and Jiang, Hansheng}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {1675--1683}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/ye24b/ye24b.pdf}, url = {https://proceedings.mlr.press/v238/ye24b.html}, abstract = { We study the dynamic pricing problem where the demand function is nonparametric and Hölder smooth, and we focus on adaptivity to the unknown Hölder smoothness parameter $\beta$ of the demand function. Traditionally the optimal dynamic pricing algorithm heavily relies on the knowledge of $\beta$ to achieve a minimax optimal regret of $\widetilde{O}(T^{\frac{\beta+1}{2\beta+1}})$. 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 $\beta$. 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 $\Omega(T^{\frac{\beta+1}{2\beta+1}})$. 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 $\beta$. } }
Endnote
%0 Conference Paper %T Smoothness-Adaptive Dynamic Pricing with Nonparametric Demand Learning %A Zeqi Ye %A Hansheng Jiang %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-ye24b %I PMLR %P 1675--1683 %U https://proceedings.mlr.press/v238/ye24b.html %V 238 %X We study the dynamic pricing problem where the demand function is nonparametric and Hölder smooth, and we focus on adaptivity to the unknown Hölder smoothness parameter $\beta$ of the demand function. Traditionally the optimal dynamic pricing algorithm heavily relies on the knowledge of $\beta$ to achieve a minimax optimal regret of $\widetilde{O}(T^{\frac{\beta+1}{2\beta+1}})$. 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 $\beta$. 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 $\Omega(T^{\frac{\beta+1}{2\beta+1}})$. 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 $\beta$.
APA
Ye, Z. & Jiang, H.. (2024). Smoothness-Adaptive Dynamic Pricing with Nonparametric Demand Learning . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:1675-1683 Available from https://proceedings.mlr.press/v238/ye24b.html.

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