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 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 ˜O(Tβ+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 Ω(Tβ+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.

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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