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Towards a Practical, Budget-Oblivious Algorithm for the Adwords Problem Under Small Bids

Author Vijay V. Vazirani

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Vijay V. Vazirani
  • University of California, Irvine, CA, USA

Funding

  • Vazirani, Vijay V.: Supported in part by NSF grant CCF-2230414.

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Vijay V. Vazirani. Towards a Practical, Budget-Oblivious Algorithm for the Adwords Problem Under Small Bids. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.FSTTCS.2023.21

Abstract

Motivated by recent insights into the online bipartite matching problem (OBM), our goal was to extend the optimal algorithm for it, namely Ranking, all the way to the special case of adwords problem, called Small, in which bids are small compared to budgets; the latter has been of considerable practical significance in ad auctions [Mehta et al., 2007]. The attractive feature of our approach was that it would yield a budget-oblivious algorithm, i.e., the algorithm would not need to know budgets of advertisers and therefore could be used in autobidding platforms. 
We were successful in obtaining an optimal, budget-oblivious algorithm for Single-Valued, under which each advertiser can make bids of one value only. However, our next extension, to Small, failed because of a fundamental reason, namely failure of the No-Surpassing Property. Since the probabilistic ideas underlying our algorithm are quite substantial, we have stated them formally, after assuming the No-Surpassing Property, and we leave the open problem of removing this assumption. 
With the help of two undergrads, we conducted extensive experiments on our algorithm on randomly generated instances. Our findings are that the No-Surpassing Property fails less than 2% of the time and that the performance of our algorithms for Single-Valued and Small are comparable to that of [Mehta et al., 2007]. If further experiments confirm this, our algorithm may be useful as such in practice, especially because of its budget-obliviousness.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic mechanism design
Keywords
  • Adwords problem
  • ad auctions
  • online bipartite matching
  • competitive analysis

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References

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