IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v68y2022i12p8568-8588.html
   My bibliography  Save this article

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

Author

Listed:
  • Jinzhi Bu

    (Department of Logistics and Maritime Studies, Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

  • David Simchi-Levi

    (Institute for Data, Systems, and Society, Department of Civil and Environmental Engineering, and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Yunzong Xu

    (Institute for Data, Systems, and Society and Statistics and Data Science Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

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 before the start of the selling horizon, the seller already has some pre-existing offline data. The offline data set contains n samples, each of which is an input-output pair consisting of a historical price and an associated demand observation. The seller wants to use both the pre-existing offline data and the sequentially revealed 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. Specifically, the size , location , and dispersion of the offline data are measured by the number of historical samples, the distance between the average historical price and the optimal price, and the standard deviation of the historical prices, respectively. For both single-historical-price setting and multiple-historical-price setting, we design a learning algorithm based on the “Optimism in the Face of Uncertainty” principle, which strikes a balance between exploration and exploitation and achieves the optimal regret up to a logarithmic factor. 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 .

Suggested Citation

  • Jinzhi Bu & David Simchi-Levi & Yunzong Xu, 2022. "Online Pricing with Offline Data: Phase Transition and Inverse Square Law," Management Science, INFORMS, vol. 68(12), pages 8568-8588, December.
  • Handle: RePEc:inm:ormnsc:v:68:y:2022:i:12:p:8568-8588
    DOI: 10.1287/mnsc.2022.4322
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.2022.4322
    Download Restriction: no

    File URL: https://libkey.io/10.1287/mnsc.2022.4322?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Gah-Yi Ban & N. Bora Keskin, 2021. "Personalized Dynamic Pricing with Machine Learning: High-Dimensional Features and Heterogeneous Elasticity," Management Science, INFORMS, vol. 67(9), pages 5549-5568, September.
    2. Arnoud V. den Boer, 2014. "Dynamic Pricing with Multiple Products and Partially Specified Demand Distribution," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 863-888, August.
    3. Mila Nambiar & David Simchi-Levi & He Wang, 2019. "Dynamic Learning and Pricing with Model Misspecification," Management Science, INFORMS, vol. 65(11), pages 4980-5000, November.
    4. Zizhuo Wang & Shiming Deng & Yinyu Ye, 2014. "Close the Gaps: A Learning-While-Doing Algorithm for Single-Product Revenue Management Problems," Operations Research, INFORMS, vol. 62(2), pages 318-331, April.
    5. Paat Rusmevichientong & John N. Tsitsiklis, 2010. "Linearly Parameterized Bandits," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 395-411, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sarkar, Biswajit & Dey, Bikash Koli, 2023. "Is online-to-offline customer care support essential for consumer service?," Journal of Retailing and Consumer Services, Elsevier, vol. 75(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Boxiao Chen & David Simchi-Levi & Yining Wang & Yuan Zhou, 2022. "Dynamic Pricing and Inventory Control with Fixed Ordering Cost and Incomplete Demand Information," Management Science, INFORMS, vol. 68(8), pages 5684-5703, August.
    2. Wang Chi Cheung & David Simchi-Levi & He Wang, 2017. "Technical Note—Dynamic Pricing and Demand Learning with Limited Price Experimentation," Operations Research, INFORMS, vol. 65(6), pages 1722-1731, December.
    3. David Simchi-Levi & Rui Sun & Huanan Zhang, 2022. "Online Learning and Optimization for Revenue Management Problems with Add-on Discounts," Management Science, INFORMS, vol. 68(10), pages 7402-7421, October.
    4. Hamsa Bastani & David Simchi-Levi & Ruihao Zhu, 2022. "Meta Dynamic Pricing: Transfer Learning Across Experiments," Management Science, INFORMS, vol. 68(3), pages 1865-1881, March.
    5. Thomas Loots & Arnoud V. den Boer, 2023. "Data‐driven collusion and competition in a pricing duopoly with multinomial logit demand," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1169-1186, April.
    6. Boxiao Chen & Xiuli Chao & Cong Shi, 2021. "Nonparametric Learning Algorithms for Joint Pricing and Inventory Control with Lost Sales and Censored Demand," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 726-756, May.
    7. Yining Wang & Boxiao Chen & David Simchi-Levi, 2021. "Multimodal Dynamic Pricing," Management Science, INFORMS, vol. 67(10), pages 6136-6152, October.
    8. Stefanus Jasin, 2014. "Reoptimization and Self-Adjusting Price Control for Network Revenue Management," Operations Research, INFORMS, vol. 62(5), pages 1168-1178, October.
    9. Woonghee Tim Huh & Michael Jong Kim & Meichun Lin, 2022. "Bayesian dithering for learning: Asymptotically optimal policies in dynamic pricing," Production and Operations Management, Production and Operations Management Society, vol. 31(9), pages 3576-3593, September.
    10. N. Bora Keskin & Assaf Zeevi, 2017. "Chasing Demand: Learning and Earning in a Changing Environment," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 277-307, May.
    11. Yining Wang & Xi Chen & Xiangyu Chang & Dongdong Ge, 2021. "Uncertainty Quantification for Demand Prediction in Contextual Dynamic Pricing," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1703-1717, June.
    12. Jianqing Fan & Yongyi Guo & Mengxin Yu, 2021. "Policy Optimization Using Semi-parametric Models for Dynamic Pricing," Papers 2109.06368, arXiv.org, revised May 2022.
    13. Arnoud V. den Boer & Bert Zwart, 2015. "Dynamic Pricing and Learning with Finite Inventories," Operations Research, INFORMS, vol. 63(4), pages 965-978, August.
    14. Jianyu Xu & Yu-Xiang Wang, 2023. "Pricing with Contextual Elasticity and Heteroscedastic Valuation," Papers 2312.15999, arXiv.org.
    15. Sentao Miao & Xi Chen & Xiuli Chao & Jiaxi Liu & Yidong Zhang, 2022. "Context‐based dynamic pricing with online clustering," Production and Operations Management, Production and Operations Management Society, vol. 31(9), pages 3559-3575, September.
    16. Qi Feng & J. George Shanthikumar, 2022. "Developing operations management data analytics," Production and Operations Management, Production and Operations Management Society, vol. 31(12), pages 4544-4557, December.
    17. Arnoud V. den Boer & N. Bora Keskin, 2022. "Dynamic Pricing with Demand Learning and Reference Effects," Management Science, INFORMS, vol. 68(10), pages 7112-7130, October.
    18. Mark Egan & Tomas Philipson, 2016. "Health Care Adherence and Personalized Medicine," Working Papers 2016-H01, Becker Friedman Institute for Research In Economics.
    19. Rong Jin & David Simchi-Levi & Li Wang & Xinshang Wang & Sen Yang, 2021. "Shrinking the Upper Confidence Bound: A Dynamic Product Selection Problem for Urban Warehouses," Management Science, INFORMS, vol. 67(8), pages 4756-4771, August.
    20. Athanassios N. Avramidis & Arnoud V. Boer, 2021. "Dynamic pricing with finite price sets: a non-parametric approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 1-34, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:68:y:2022:i:12:p:8568-8588. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.