Stochastic Models for Budget Optimization in Search-Based Advertising

  • S. Muthukrishnan
  • Martin Pál
  • Zoya Svitkina
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4858)


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.


Stochastic Model Knapsack Problem Online Algorithm Integer Solution Scenario Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Aggarwal, G., Goel, A., Motwani, R.: Truthful auctions for pricing search keywords. In: Proc. 8th ACM Conf. on Electronic Commerce, pp. 1–7 (2006)Google Scholar
  2. 2.
    Babaioff, M., Immorlica, N., Kempe, D., Kleinberg, R.: A knapsack secretary problem with applications. In: Proc. 10th APPROX (2007)Google Scholar
  3. 3.
    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)Google Scholar
  4. 4.
    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)Google Scholar
  5. 5.
    Carraway, R.L., Schmidt, R.L., Weatherford, L.R.: An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns. Naval Research Logistics 40, 161–173 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chakrabarty, D., Zhou, Y., Lukose, R.: Budget constrained bidding in keyword auctions and online knapsack problems. In: WWW 2007 Workshop on Sponsored Search Auctions (2007)Google Scholar
  7. 7.
    Charikar, M., Chekuri, C., Pal, M.: Sampling bounds for stochastic optimization. In: Proc. 9th International Workshop on Randomization and Computation (2005)Google Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    Feldman, J., Muthukrishnan, S., Pal, M., Stein, C.: Budget optimization in search-based advertising auctions. In: Proc. 9th ACM Conf. on Electronic Commerce (2007)Google Scholar
  10. 10.
    Goel, A., Indyk, P.: Stochastic load balancing and related problems. In: Proc. 40th IEEE Symp. on Foundations of Computer Science (1999)Google Scholar
  11. 11.
    Henig, M.I.: Risk criteria in a stochastic knapsack problem. Oper. Res. 38(5), 820–825 (1990)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kleinberg, J., Rabani, Y., Tardos, E.: Allocating bandwidth for bursty connections. SIAM Journal on Computing 30(1), 191–217 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Kleywegt, A.J., Shapiro, A., Homem-de-Mello, T.: The sample average approximation method for stochastic discrete optimization. SIAM J. on Optimization 12, 479–502 (2002)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Mahdian, M., Nazerzadeh, H., Saberi, A.: Allocating online advertisement space with unreliable estimates. In: Proc. 9th ACM Conf. on Electronic Commerce (2007)Google Scholar
  15. 15.
    Mehta, A., Saberi, A., Vazirani, U., Vazirani, V.: Adwords and generalized on-line matching. In: Proc. 46th IEEE Symp. on Foundations of Computer Science, pp. 264–273 (2005)Google Scholar
  16. 16.
    Ostrovsky, M., Edelman, B., Schwarz, M.: Internet advertising and the generalized second price auction: Selling billions of dollars worth of keywords (forthcoming). American Economic Review  (2006)Google Scholar
  17. 17.
    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)Google Scholar
  18. 18.
    Sniedovich, M.: Preference order stochastic knapsack problems: Methodological issues. The Journal of the Operational Research Society 31, 1025–1032 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Steinberg, E., Parks, M.: A preference order dynamic program for a knapsack problem with stochastic rewards. The Journal of the Operational Research Society 30(2), 141–147 (1979)zbMATHCrossRefGoogle Scholar
  20. 20.
    Swamy, C., Shmoys, D.B.: Approximation algorithms for 2-stage stochastic optimization problems. SIGACT News 37(1), 33–46 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • S. Muthukrishnan
    • 1
  • Martin Pál
    • 1
  • Zoya Svitkina
    • 2
  1. 1.Google, Inc., New York, NY 
  2. 2.Department of Computer Science, Dartmouth College 

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