IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v67y2020i5p368-379.html
   My bibliography  Save this article

Technical note: Finite‐time regret analysis of Kiefer‐Wolfowitz stochastic approximation algorithm and nonparametric multi‐product dynamic pricing with unknown demand

Author

Listed:
  • L. Jeff Hong
  • Chenghuai Li
  • Jun Luo

Abstract

We consider the problem of nonparametric multi‐product dynamic pricing with unknown demand and show that the problem may be formulated as an online model‐free stochastic program, which can be solved by the classical Kiefer‐Wolfowitz stochastic approximation (KWSA) algorithm. We prove that the expected cumulative regret of the KWSA algorithm is bounded above by κ1T+κ2 where κ1, κ2 are positive constants and T is the number of periods for any T = 1, 2, …. Therefore, the regret of the KWSA algorithm grows in the order of T, which achieves the lower bounds known for parametric dynamic pricing problems and shows that the nonparametric problems are not necessarily more difficult to solve than the parametric ones. Numerical experiments further demonstrate the effectiveness and efficiency of our proposed KW pricing policy by comparing with some pricing policies in the literature.

Suggested Citation

  • L. Jeff Hong & Chenghuai Li & Jun Luo, 2020. "Technical note: Finite‐time regret analysis of Kiefer‐Wolfowitz stochastic approximation algorithm and nonparametric multi‐product dynamic pricing with unknown demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(5), pages 368-379, August.
    • Handle: RePEc:wly:navres:v:67:y:2020:i:5:p:368-379
    DOI: 10.1002/nav.21902
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21902
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21902?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. Arnoud V. den Boer & Bert Zwart, 2014. "Simultaneously Learning and Optimizing Using Controlled Variance Pricing," Management Science, INFORMS, vol. 60(3), pages 770-783, March.
    2. J. Michael Harrison & N. Bora Keskin & Assaf Zeevi, 2012. "Bayesian Dynamic Pricing Policies: Learning and Earning Under a Binary Prior Distribution," Management Science, INFORMS, vol. 58(3), pages 570-586, March.
    3. N. Bora Keskin & Assaf Zeevi, 2014. "Dynamic Pricing with an Unknown Demand Model: Asymptotically Optimal Semi-Myopic Policies," Operations Research, INFORMS, vol. 62(5), pages 1142-1167, October.
    4. Omar Besbes & Assaf Zeevi, 2015. "On the (Surprising) Sufficiency of Linear Models for Dynamic Pricing with Demand Learning," Management Science, INFORMS, vol. 61(4), pages 723-739, April.
    5. Josef Broder & Paat Rusmevichientong, 2012. "Dynamic Pricing Under a General Parametric Choice Model," Operations Research, INFORMS, vol. 60(4), pages 965-980, August.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Huashuai Qu & Ilya O. Ryzhov & Michael C. Fu & Eric Bergerson & Megan Kurka & Ludek Kopacek, 2020. "Learning Demand Curves in B2B Pricing: A New Framework and Case Study," Production and Operations Management, Production and Operations Management Society, vol. 29(5), pages 1287-1306, May.
    3. den Boer, Arnoud V., 2015. "Tracking the market: Dynamic pricing and learning in a changing environment," European Journal of Operational Research, Elsevier, vol. 247(3), pages 914-927.
    4. Ruben Geer & Arnoud V. Boer & Christopher Bayliss & Christine S. M. Currie & Andria Ellina & Malte Esders & Alwin Haensel & Xiao Lei & Kyle D. S. Maclean & Antonio Martinez-Sykora & Asbjørn Nilsen Ris, 2019. "Dynamic pricing and learning with competition: insights from the dynamic pricing challenge at the 2017 INFORMS RM & pricing conference," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 18(3), pages 185-203, June.
    5. 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.
    6. 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.
    7. Yang, Chaolin & Xiong, Yi, 2020. "Nonparametric advertising budget allocation with inventory constraint," European Journal of Operational Research, Elsevier, vol. 285(2), pages 631-641.
    8. 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.
    9. Ying Zhong & L. Jeff Hong & Guangwu Liu, 2021. "Earning and Learning with Varying Cost," Production and Operations Management, Production and Operations Management Society, vol. 30(8), pages 2379-2394, August.
    10. Ruben van de Geer & Arnoud V. den Boer & Christopher Bayliss & Christine Currie & Andria Ellina & Malte Esders & Alwin Haensel & Xiao Lei & Kyle D. S. Maclean & Antonio Martinez-Sykora & Asbj{o}rn Nil, 2018. "Dynamic Pricing and Learning with Competition: Insights from the Dynamic Pricing Challenge at the 2017 INFORMS RM & Pricing Conference," Papers 1804.03219, arXiv.org.
    11. Xi Chen & Jianjun Gao & Dongdong Ge & Zizhuo Wang, 2022. "Bayesian dynamic learning and pricing with strategic customers," Production and Operations Management, Production and Operations Management Society, vol. 31(8), pages 3125-3142, August.
    12. 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.
    13. William L. Cooper & Tito Homem-de-Mello & Anton J. Kleywegt, 2015. "Learning and Pricing with Models That Do Not Explicitly Incorporate Competition," Operations Research, INFORMS, vol. 63(1), pages 86-103, February.
    14. 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.
    15. Athanassios N. Avramidis, 2020. "A pricing problem with unknown arrival rate and price sensitivity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 77-106, August.
    16. Yuqing Zhang & Neil Walton, 2019. "Adaptive Pricing in Insurance: Generalized Linear Models and Gaussian Process Regression Approaches," Papers 1907.05381, arXiv.org.
    17. Gur, Yonatan & Macnamara, Gregory & Saban, Daniela, 2020. "On the Disclosure of Promotion Value in Platforms with Learning Sellers," Research Papers 3865, Stanford University, Graduate School of Business.
    18. Omar Besbes & Assaf Zeevi, 2015. "On the (Surprising) Sufficiency of Linear Models for Dynamic Pricing with Demand Learning," Management Science, INFORMS, vol. 61(4), pages 723-739, April.
    19. Arnoud V. den Boer & N. Bora Keskin, 2020. "Discontinuous Demand Functions: Estimation and Pricing," Management Science, INFORMS, vol. 66(10), pages 4516-4534, October.
    20. Jianqing Fan & Yongyi Guo & Mengxin Yu, 2021. "Policy Optimization Using Semi-parametric Models for Dynamic Pricing," Papers 2109.06368, arXiv.org, revised May 2022.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:67:y:2020:i:5:p:368-379. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.