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Online Allocation and Display Ads Optimization with Surplus Supply

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Web and Internet Economics (WINE 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13778))

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Abstract

In this work, we study a scenario where a publisher seeks to maximize its total revenue across two sales channels: guaranteed contracts that promise to deliver a certain number of impressions to the advertisers, and spot demands through an Ad Exchange. On the one hand, if a guaranteed contract is not fully delivered, it incurs a penalty for the publisher. On the other hand, the publisher might be able to sell an impression at a high price in the Ad Exchange. How does a publisher maximize its total revenue as a sum of the revenue from the Ad Exchange and the loss from the under-delivery penalty? We study this problem parameterized by supply factor f: a notion we introduce that, intuitively, captures the number of times a publisher can satisfy all its guaranteed contracts given its inventory supply. In this work we present a fast simple deterministic algorithm with the optimal competitive ratio. The algorithm and the optimal competitive ratio are a function of the supply factor, penalty, and the distribution of the bids in the Ad Exchange.

Beyond the yield optimization problem, classic online allocation problems such as online bipartite matching of Karp-Vazirani-Vazirani [25] and its vertex-weighted variant of Aggarwal et al. [2] can be studied in the presence of the additional supply guaranteed by the supply factor. We show that a supply factor of f improves the approximation factors from \(1-1/e\) to \(f-fe^{-1/f}\). Our approximation factor is tight and approaches 1 as \(f \rightarrow \infty \).

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Notes

  1. 1.

    We use the terms demand and capacity interchangeably. Technically, offline nodes do not have any capacities, they just have demands. However, for a node that demands \(n_a\) impressions, assigning more than \(n_a\) impressions is always suboptimal, so essentially \(n_a\) can be interpreted as a capacity as well. The AdEx offline node is an exception where the capacity is infinite, in the sense that it is always profitable to assign an additional online node to AdEx.

  2. 2.

    We later discuss relaxing the penalty c to depend on the advertiser a.

  3. 3.

    Unweighted edges for contractual advertisers is fine because these contracts are mostly based on the number of impressions delivered. In a few cases the contracts are based on the number of clicks or conversions, in which case the edges will be weighted based on the probability of click or conversion. Contracts based on impressions form such a large majority, that having unweighted edges, is almost wlog.

  4. 4.

    Note that \(A_j\) is a random set depending on the realization of AdEx rewards over all queries.

  5. 5.

    The assumption on a fixed support, can be relaxed using a standard discretization approach at a small cost in the competitive ratio that depends on this discretization.

References

  1. Aggarwal, G., Cai, Y., Mehta, A., Pierrakos, G.: Biobjective online bipartite matching. In: Liu, T.-Y., Qi, Q., Ye, Y. (eds.) WINE 2014. LNCS, vol. 8877, pp. 218–231. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13129-0_16

    Chapter  Google Scholar 

  2. Aggarwal, G., Goel, G., Karande, C., Mehta, A.: Online vertex-weighted bipartite matching and single-bid budgeted allocations. In: Randall, D. (ed.) Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, San Francisco, California, USA, 23–25 January 2011, pp. 1253–1264. SIAM (2011)

    Google Scholar 

  3. Agrawal, S., Devanur, N.R.: Fast algorithms for online stochastic convex programming. In: Indyk, P. (ed.) Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, 4–6 January 2015, pp. 1405–1424. SIAM (2015)

    Google Scholar 

  4. Agrawal, S., Wang, Z., Ye, Y.: A dynamic near-optimal algorithm for online linear programming. Oper. Res. 62(4), 876–890 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Balseiro, S.R., Feldman, J., Mirrokni, V.S., Muthukrishnan, S.: Yield optimization of display advertising with ad exchange. Manag. Sci. 60(12), 2886–2907 (2014)

    Article  Google Scholar 

  6. Balseiro, S.R., Lu, H., Mirrokni, V.S.: Dual mirror descent for online allocation problems. In: Proceedings of the 37th International Conference on Machine Learning, ICML 2020, July 13–18 2020, Virtual Event. Proceedings of Machine Learning Research, vol. 119, pp. 613–628. PMLR (2020)

    Google Scholar 

  7. Blanc, G., Charikar, M.: Multiway online correlated selection. In: 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS), pp. 1277–1284. IEEE (2022)

    Google Scholar 

  8. Choi, H., Mela, C.F., Balseiro, S.R., Leary, A.: Online display advertising markets: a literature review and future directions. Inf. Syst. Res. 31(2), 556–575 (2020)

    Article  Google Scholar 

  9. Cohen, I.R., Wajc, D.: Randomized online matching in regular graphs. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 960–979. SIAM (2018)

    Google Scholar 

  10. Derakhshan, M., Golrezaei, N., Leme, R.P.: Lp-based approximation for personalized reserve prices. In: Karlin, A., Immorlica, N., Johari, R. (eds.) Proceedings of the 2019 ACM Conference on Economics and Computation, EC 2019, Phoenix, AZ, USA, 24–28 June 2019, p. 589. ACM (2019)

    Google Scholar 

  11. Devanur, N.R., Hayes, T.P.: The adwords problem: online keyword matching with budgeted bidders under random permutations. In: Chuang, J., Fortnow, L., Pu, P. (eds.) Proceedings 10th ACM Conference on Electronic Commerce (EC-2009), Stanford, California, USA, 6–10 July 2009, pp. 71–78. ACM (2009)

    Google Scholar 

  12. Devanur, N.R., Jain, K.: Online matching with concave returns. In: Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing, pp. 137–144 (2012)

    Google Scholar 

  13. Devanur, N.R., Jain, K., Kleinberg, R.D.: Randomized primal-dual analysis of RANKING for online bipartite matching. In: Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013, New Orleans, Louisiana, USA, 6–8 January 2013, pp. 101–107. SIAM (2013)

    Google Scholar 

  14. Devanur, N.R., Jain, K., Sivan, B., Wilkens, C.A.: Near optimal online algorithms and fast approximation algorithms for resource allocation problems. J. ACM 66(1), 7:1-7:41 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  15. Dvoák, W., Henzinger, M.: Online ad assignment with an ad exchange. In: Bampis, E., Svensson, O. (eds.) WAOA 2014. LNCS, vol. 8952, pp. 156–167. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-18263-6_14

    Chapter  Google Scholar 

  16. Esfandiari, H., Korula, N., Mirrokni, V.: Bi-objective online matching and submodular allocations. Adv. Neural. Inf. Process. Syst. 29, 2739–2747 (2016)

    Google Scholar 

  17. Esfandiari, H., Korula, N., Mirrokni, V.: Allocation with traffic spikes: mixing adversarial and stochastic models. ACM Trans. Econ. Comput. (TEAC) 6(3–4), 1–23 (2018)

    MathSciNet  Google Scholar 

  18. Fahrbach, M., Huang, Z., Tao, R., Zadimoghaddam, M.: Edge-weighted online bipartite matching. In: 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), pp. 412–423. IEEE (2020)

    Google Scholar 

  19. Feldman, J., Henzinger, M., Korula, N., Mirrokni, V.S., Stein, C.: Online stochastic packing applied to display ad allocation. In: de Berg, M., Meyer, U. (eds.) ESA 2010. LNCS, vol. 6346, pp. 182–194. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15775-2_16

    Chapter  Google Scholar 

  20. Feldman, J., Korula, N., Mirrokni, V., Muthukrishnan, S., Pál, M.: Online ad assignment with free disposal. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 374–385. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10841-9_34

    Chapter  Google Scholar 

  21. Gao, R., He, Z., Huang, Z., Nie, Z., Yuan, B., Zhong, Y.: Improved online correlated selection. In: 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS), pp. 1265–1276. IEEE (2022)

    Google Scholar 

  22. Huang, Z., Zhang, Q., Zhang, Y.: Adwords in a panorama. In: 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020, Durham, NC, USA, 16–19 November 2020, pp. 1416–1426. IEEE (2020)

    Google Scholar 

  23. Kalyanasundaram, B., Pruhs, K.: An optimal deterministic algorithm for online b-matching. Theor. Comput. Sci. 233(1–2), 319–325 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  24. Karande, C., Mehta, A., Tripathi, P.: Online bipartite matching with unknown distributions. In: Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing, pp. 587–596 (2011)

    Google Scholar 

  25. Karp, R.M., Vazirani, U.V., Vazirani, V.V.: An optimal algorithm for on-line bipartite matching. In: Proceedings of the Twenty-Second Annual ACM Symposium on Theory of Computing, pp. 352–358 (1990)

    Google Scholar 

  26. Korula, N., Mirrokni, V.S., Zadimoghaddam, M.: Bicriteria online matching: maximizing weight and cardinality. In: Chen, Y., Immorlica, N. (eds.) WINE 2013. LNCS, vol. 8289, pp. 305–318. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-45046-4_25

    Chapter  MATH  Google Scholar 

  27. Leme, R.P., Pál, M., Vassilvitskii, S.: A field guide to personalized reserve prices. In: Bourdeau, J., Hendler, J., Nkambou, R., Horrocks, I., Zhao, B.Y. (eds.) Proceedings of the 25th International Conference on World Wide Web, WWW 2016, Montreal, Canada, 11–15 April 2016, pp. 1093–1102. ACM (2016)

    Google Scholar 

  28. Mehta, A.: Online matching and ad allocation. Found. Trends Theor. Comput. Sci. 8(4), 265–368 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  29. Mehta, A., Saberi, A., Vazirani, U., Vazirani, V.: Adwords and generalized online matching. Journal of the ACM (JACM) 54(5), 22-es (2007)

    Google Scholar 

  30. Mirrokni, V.S., Gharan, S.O., Zadimoghaddam, M.: Simultaneous approximations for adversarial and stochastic online budgeted allocation. In: Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012, Kyoto, Japan, January 17–19, 2012. pp. 1690–1701. SIAM (2012)

    Google Scholar 

  31. Naor, J., Wajc, D.: Near-optimum online ad allocation for targeted advertising. ACM Transactions on Economics and Computation (TEAC) 6(3–4), 1–20 (2018)

    MathSciNet  Google Scholar 

  32. Shin, Y., An, H.C.: Making three out of two: Three-way online correlated selection. arXiv preprint arXiv:2107.02605 (2021)

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Authors and Affiliations

  1. Google, New York, NY, USA

    Melika Abolhassani, Hossein Esfandiari, Balasubramanian Sivan, Yifeng Teng & Creighton Thomas

  2. University of Salzberg, Salzburg, Austria

    Yasamin Nazari

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  1. Melika Abolhassani
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  2. Hossein Esfandiari
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  4. Balasubramanian Sivan
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  5. Yifeng Teng
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Correspondence to Yifeng Teng .

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Editors and Affiliations

  1. Aarhus University, Aarhus, Denmark

    Kristoffer Arnsfelt Hansen

  2. Tsinghua University, Beijing, China

    Tracy Xiao Liu

  3. Rotman School of Management, University of Toronto, Toronto, ON, Canada

    Azarakhsh Malekian

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Abolhassani, M., Esfandiari, H., Nazari, Y., Sivan, B., Teng, Y., Thomas, C. (2022). Online Allocation and Display Ads Optimization with Surplus Supply. In: Hansen, K.A., Liu, T.X., Malekian, A. (eds) Web and Internet Economics. WINE 2022. Lecture Notes in Computer Science, vol 13778. Springer, Cham. https://doi.org/10.1007/978-3-031-22832-2_3

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  • DOI: https://doi.org/10.1007/978-3-031-22832-2_3

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