Skip to main content
Log in

Stochastic Models for Budget Optimization in Search-Based Advertising

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

Internet search companies sell advertisement slots based on users’ search queries via an auction. Advertisers have to determine how to place bids on the keywords of their interest in order to maximize their return for a given budget: this is the budget optimization problem. The solution depends on the distribution of future queries. In this paper, we formulate stochastic versions of the budget optimization problem based on natural probabilistic models of distribution over future queries, and address two questions that arise.

Evaluation :

Given a solution, can we evaluate the expected value of the objective function?

Optimization :

Can we find a solution that maximizes the objective function in expectation?

Our main results are approximation and complexity results for these two problems in our three stochastic models. In particular, our algorithmic results show that simple prefix strategies that bid on all cheap keywords up to some level are either optimal or good approximations for many cases; we show other cases to be NP-hard.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kleywegt, A.J., Shapiro, A., Homem-de-Mello, T.: The sample average approximation method for stochastic discrete optimization. SIAM J. Optim. 12(2), 479–502 (2002)

    Article  MathSciNet  Google Scholar 

  2. Charikar, M., Chekuri, C., Pal, M.: Sampling bounds for stochastic optimization. In: Proc. 9th International Workshop on Randomization and Computation (2005)

  3. Swamy, C., Shmoys, D.B.: Approximation algorithms for 2-stage stochastic optimization problems. SIGACT News 37(1), 33–46 (2006)

    Article  Google Scholar 

  4. Feldman, J., Muthukrishnan, S., Pal, M., Stein, C.: Budget optimization in search-based advertising auctions. In: Proc. 9th ACM Conf. on Electronic Commerce (2007)

  5. Dean, B.C., Goemans, M.X., Vondrak, J.: Approximating the stochastic knapsack problem: the benefit of adaptivity. In: Proc. 45th IEEE Symp. on Foundations of Computer Science, pp. 208–217 (2004)

  6. Kleinberg, J., Rabani, Y., Tardos, E.: Allocating bandwidth for bursty connections. SIAM J. Comput. 30(1), 191–217 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Goel, A., Indyk, P.: Stochastic load balancing and related problems. In: Proc. 40th IEEE Symp. on Foundations of Computer Science (1999)

  8. Carraway, R.L., Schmidt, R.L., Weatherford, L.R.: An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns. Nav. Res. Logist. 40, 161–173 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  9. Henig, M.I.: Risk criteria in a stochastic knapsack problem. Oper. Res. 38(5), 820–825 (1990)

    Article  MathSciNet  Google Scholar 

  10. Sniedovich, M.: Preference order stochastic knapsack problems: methodological issues. J. Oper. Res. Soc. 31(11), 1025–1032 (1980)

    MATH  MathSciNet  Google Scholar 

  11. Steinberg, E., Parks, M.: A preference order dynamic program for a knapsack problem with stochastic rewards. J. Oper. Res. Soc. 30(2), 141–147 (1979)

    MATH  Google Scholar 

  12. Chakrabarty, D., Zhou, Y., Lukose, R.: Budget constrained bidding in keyword auctions and online knapsack problems. In: WWW2007 Workshop on Sponsored Search Auctions (2007)

  13. Babaioff, M., Immorlica, N., Kempe, D., Kleinberg, R.: A knapsack secretary problem with applications. In: Proc. 10th APPROX (2007)

  14. Rusmevichientong, P., Williamson, D.P.: An adaptive algorithm for selecting profitable keywords for search-based advertising services. In: Proc. 8th ACM Conf. on Electronic Commerce, pp. 260–269 (2006)

  15. Ostrovsky, M., Edelman, B., Schwarz, M.: Internet advertising and the generalized second price auction: selling billions of dollars worth of keywords. Am. Econ. Rev. 97(1) (2007)

  16. Aggarwal, G., Goel, A., Motwani, R.: Truthful auctions for pricing search keywords. In: Proc. 8th ACM Conf. on Electronic Commerce, pp. 1–7 (2006)

  17. Borgs, C., Chayes, J., Immorlica, N., Mahdian, M., Saberi, A.: Multi-unit auctions with budget-constrained bidders. In: Proc. 7th ACM Conf. on Electronic Commerce, pp. 44–51 (2005)

  18. Borgs, C., Chayes, J., Etesami, O., Immorlica, N., Jain, K., Mahdian, M.: Bid optimization in online advertisement auctions. In: 16th International World Wide Web Conference (2007)

  19. Mehta, A., Saberi, A., Vazirani, U., Vazirani, V.: Adwords and generalized online matching. J. ACM 54(5) (2007)

  20. Mahdian, M., Nazerzadeh, H., Saberi, A.: Allocating online advertisement space with unreliable estimates. In: Proc. 9th ACM Conf. on Electronic Commerce (2007)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zoya Svitkina.

Additional information

Preliminary versions of this paper appeared in the WWW Workshop on Sponsored Search, 2007, and the Third International Workshop on Internet and Network Economics (WINE 2007).

This work was done while Z. Svitkina was visiting Google, Inc., New York, NY.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Muthukrishnan, S., Pál, M. & Svitkina, Z. Stochastic Models for Budget Optimization in Search-Based Advertising. Algorithmica 58, 1022–1044 (2010). https://doi.org/10.1007/s00453-009-9311-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00453-009-9311-6

Keywords

Navigation