Learning Submodular Functions

  • Maria-Florina Balcan
  • Nicholas J. A. Harvey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7524)


Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications that have been used in many areas, including combinatorial optimization, machine learning, and economics. In this work we use a learning theoretic angle for studying submodular functions. We provide algorithms for learning submodular functions, as well as lower bounds on their learnability. In doing so, we uncover several novel structural results revealing both extremal properties as well as regularities of submodular functions, of interest to many areas.


Boolean Function Approximation Factor Valuation Function Combinatorial Auction Submodular Function 
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.


  1. 1.
    NIPS workshop on discrete optimization in machine learning: Submodularity, sparsity & polyhedra, DISCML (2009),
  2. 2.
    NIPS workshop on discrete optimization in machine learning (discml): Uncertainty, generalization and feedback (2011),
  3. 3.
    Balcan, M.F., Blum, A., Mansour, Y.: Item pricing for revenue maxmimization. In: ACM Conference on Electronic Commerce (2009)Google Scholar
  4. 4.
    Blum, A., Burch, C., Langford, J.: On learning monotone boolean functions. In: FOCS (1998)Google Scholar
  5. 5.
    Dachman-Soled, D., Lee, H.K., Malkin, T., Servedio, R.A., Wan, A., Wee, H.M.: Optimal Cryptographic Hardness of Learning Monotone Functions. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 36–47. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Dobzinski, S., Nisan, N., Schapira, M.: Truthful Randomized Mechanisms for Combinatorial Auctions. In: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, pp. 644–652 (2006)Google Scholar
  7. 7.
    Goemans, M., Harvey, N., Iwata, S., Mirrokni, V.: Approximating submodular functions everywhere. In: ACM-SIAM Symposium on Discrete Algorithms (2009)Google Scholar
  8. 8.
    Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer (1993)Google Scholar
  9. 9.
    Krause, A., Guestrin, C.: Beyond convexity: Submodularity in machine learning (2008),
  10. 10.
    Krause, A., Guestrin, C.: Intelligent information gathering and submodular function optimization (2009),
  11. 11.
    Krause, A., Guestrin, C.: Near-optimal nonmyopic value of information in graphical models. In: UAI (2005)Google Scholar
  12. 12.
    Lehmann, B., Lehmann, D.J., Nisan, N.: Combinatorial auctions with decreasing marginal utilities. Games and Economic Behavior 55, 270–296 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Narasimhan, M., Bilmes, J.: Local search for balanced submodular clusterings. In: Twentieth International Joint Conference on Artificial Intelligence (2007)Google Scholar
  14. 14.
    Vondrák, J.: Optimal approximation for the submodular welfare problem in the value oracle model. In: STOC (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Maria-Florina Balcan
    • 1
  • Nicholas J. A. Harvey
    • 2
  1. 1.School of Computer ScienceGeorgia Institute of TechnologyUSA
  2. 2.University of British ColumbiaCanada

Personalised recommendations