Online Pricing with Offline Data: Phase Transition and Inverse Square Law

Jinzhi Bu, David Simchi-Levi, Yunzong Xu
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:1202-1210, 2020.

Abstract

This paper investigates the impact of pre-existing offline data on online learning, in the context of dynamic pricing. We study a single-product dynamic pricing problem over a selling horizon of T periods. The demand in each period is determined by the price of the product according to a linear demand model with unknown parameters. We assume that the seller already has some pre-existing offline data before the start of the selling horizon. The seller wants to utilize both the pre-existing offline data and the sequential online data to minimize the regret of the online learning process. We characterize the joint effect of the size, location and dispersion of the offline data on the optimal regret of the online learning process. Our results reveal surprising transformations of the optimal regret rate with respect to the size of the offline data, which we refer to as phase transitions. In addition, our results demonstrate that the location and dispersion of the offline data also have an intrinsic effect on the optimal regret, and we quantify this effect via the inverse-square law.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-bu20a, title = {Online Pricing with Offline Data: Phase Transition and Inverse Square Law}, author = {Bu, Jinzhi and Simchi-Levi, David and Xu, Yunzong}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {1202--1210}, year = {2020}, editor = {Hal Daumé III and Aarti Singh}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/bu20a/bu20a.pdf}, url = { http://proceedings.mlr.press/v119/bu20a.html }, abstract = {This paper investigates the impact of pre-existing offline data on online learning, in the context of dynamic pricing. We study a single-product dynamic pricing problem over a selling horizon of T periods. The demand in each period is determined by the price of the product according to a linear demand model with unknown parameters. We assume that the seller already has some pre-existing offline data before the start of the selling horizon. The seller wants to utilize both the pre-existing offline data and the sequential online data to minimize the regret of the online learning process. We characterize the joint effect of the size, location and dispersion of the offline data on the optimal regret of the online learning process. Our results reveal surprising transformations of the optimal regret rate with respect to the size of the offline data, which we refer to as phase transitions. In addition, our results demonstrate that the location and dispersion of the offline data also have an intrinsic effect on the optimal regret, and we quantify this effect via the inverse-square law.} }
Endnote
%0 Conference Paper %T Online Pricing with Offline Data: Phase Transition and Inverse Square Law %A Jinzhi Bu %A David Simchi-Levi %A Yunzong Xu %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-bu20a %I PMLR %P 1202--1210 %U http://proceedings.mlr.press/v119/bu20a.html %V 119 %X This paper investigates the impact of pre-existing offline data on online learning, in the context of dynamic pricing. We study a single-product dynamic pricing problem over a selling horizon of T periods. The demand in each period is determined by the price of the product according to a linear demand model with unknown parameters. We assume that the seller already has some pre-existing offline data before the start of the selling horizon. The seller wants to utilize both the pre-existing offline data and the sequential online data to minimize the regret of the online learning process. We characterize the joint effect of the size, location and dispersion of the offline data on the optimal regret of the online learning process. Our results reveal surprising transformations of the optimal regret rate with respect to the size of the offline data, which we refer to as phase transitions. In addition, our results demonstrate that the location and dispersion of the offline data also have an intrinsic effect on the optimal regret, and we quantify this effect via the inverse-square law.
APA
Bu, J., Simchi-Levi, D. & Xu, Y.. (2020). Online Pricing with Offline Data: Phase Transition and Inverse Square Law. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:1202-1210 Available from http://proceedings.mlr.press/v119/bu20a.html .

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