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Dynamic Budget Throttling in Repeated Second-Price Auctions

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Listed:
  • Zhaohua Chen
  • Chang Wang
  • Qian Wang
  • Yuqi Pan
  • Zhuming Shi
  • Zheng Cai
  • Yukun Ren
  • Zhihua Zhu
  • Xiaotie Deng

Abstract

In today's online advertising markets, a crucial requirement for an advertiser is to control her total expenditure within a time horizon under some budget. Among various budget control methods, throttling has emerged as a popular choice, managing an advertiser's total expenditure by selecting only a subset of auctions to participate in. This paper provides a theoretical panorama of a single advertiser's dynamic budget throttling process in repeated second-price auctions. We first establish a lower bound on the regret and an upper bound on the asymptotic competitive ratio for any throttling algorithm, respectively, when the advertiser's values are stochastic and adversarial. Regarding the algorithmic side, we propose the OGD-CB algorithm, which guarantees a near-optimal expected regret with stochastic values. On the other hand, when values are adversarial, we prove that this algorithm also reaches the upper bound on the asymptotic competitive ratio. We further compare throttling with pacing, another widely adopted budget control method, in repeated second-price auctions. In the stochastic case, we demonstrate that pacing is generally superior to throttling for the advertiser, supporting the well-known result that pacing is asymptotically optimal in this scenario. However, in the adversarial case, we give an exciting result indicating that throttling is also an asymptotically optimal dynamic bidding strategy. Our results bridge the gaps in theoretical research of throttling in repeated auctions and comprehensively reveal the ability of this popular budget-smoothing strategy.

Suggested Citation

  • Zhaohua Chen & Chang Wang & Qian Wang & Yuqi Pan & Zhuming Shi & Zheng Cai & Yukun Ren & Zhihua Zhu & Xiaotie Deng, 2022. "Dynamic Budget Throttling in Repeated Second-Price Auctions," Papers 2207.04690, arXiv.org, revised Dec 2023.
  • Handle: RePEc:arx:papers:2207.04690
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    References listed on IDEAS

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    1. Alberto Vera & Siddhartha Banerjee, 2021. "The Bayesian Prophet: A Low-Regret Framework for Online Decision Making," Management Science, INFORMS, vol. 67(3), pages 1368-1391, March.
    2. Anton J. Kleywegt & Jason D. Papastavrou, 2001. "The Dynamic and Stochastic Knapsack Problem with Random Sized Items," Operations Research, INFORMS, vol. 49(1), pages 26-41, February.
    3. Anupam Gupta & Marco Molinaro, 2016. "How the Experts Algorithm Can Help Solve LPs Online," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1404-1431, November.
    4. Stefanus Jasin & Amitabh Sinha, 2015. "An LP-Based Correlated Rounding Scheme for Multi-Item Ecommerce Order Fulfillment," Operations Research, INFORMS, vol. 63(6), pages 1336-1351, December.
    5. Jason Acimovic & Stephen C. Graves, 2015. "Making Better Fulfillment Decisions on the Fly in an Online Retail Environment," Manufacturing & Service Operations Management, INFORMS, vol. 17(1), pages 34-51, February.
    6. Pornpawee Bumpensanti & He Wang, 2020. "A Re-Solving Heuristic with Uniformly Bounded Loss for Network Revenue Management," Management Science, INFORMS, vol. 66(7), pages 2993-3009, July.
    7. Guillermo Gallego & Huseyin Topaloglu, 2019. "Revenue Management and Pricing Analytics," International Series in Operations Research and Management Science, Springer, number 978-1-4939-9606-3, April.
    8. Anton J. Kleywegt & Jason D. Papastavrou, 1998. "The Dynamic and Stochastic Knapsack Problem," Operations Research, INFORMS, vol. 46(1), pages 17-35, February.
    9. Vibhanshu Abhishek & Kartik Hosanagar, 2013. "Optimal Bidding in Multi-Item Multislot Sponsored Search Auctions," Operations Research, INFORMS, vol. 61(4), pages 855-873, August.
    10. Santiago R. Balseiro & Omar Besbes & Gabriel Y. Weintraub, 2015. "Repeated Auctions with Budgets in Ad Exchanges: Approximations and Design," Management Science, INFORMS, vol. 61(4), pages 864-884, April.
    11. Shipra Agrawal & Zizhuo Wang & Yinyu Ye, 2014. "A Dynamic Near-Optimal Algorithm for Online Linear Programming," Operations Research, INFORMS, vol. 62(4), pages 876-890, August.
    12. Zhaohua Chen & Mingwei Yang & Chang Wang & Jicheng Li & Zheng Cai & Yukun Ren & Zhihua Zhu & Xiaotie Deng, 2022. "Budget-Constrained Auctions with Unassured Priors: Strategic Equivalence and Structural Properties," Papers 2203.16816, arXiv.org, revised Feb 2024.
    13. Santiago R. Balseiro & Yonatan Gur, 2019. "Learning in Repeated Auctions with Budgets: Regret Minimization and Equilibrium," Management Science, INFORMS, vol. 65(9), pages 3952-3968, September.
    14. Stefanus Jasin & Sunil Kumar, 2012. "A Re-Solving Heuristic with Bounded Revenue Loss for Network Revenue Management with Customer Choice," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 313-345, May.
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