Online Prediction under Submodular Constraints

  • Daiki Suehiro
  • Kohei Hatano
  • Shuji Kijima
  • Eiji Takimoto
  • Kiyohito Nagano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7568)


We consider an online prediction problem of combinatorial concepts where each combinatorial concept is represented as a vertex of a polyhedron described by a submodular function (base polyhedron). In general, there are exponentially many vertices in the base polyhedron. We propose polynomial time algorithms with regret bounds. In particular, for cardinality-based submodular functions, we give O(n 2)-time algorithms.


Extreme Point Convex Combination Submodular Function Combinatorial Concept Procedure Projection 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Daiki Suehiro
    • 1
  • Kohei Hatano
    • 1
  • Shuji Kijima
    • 1
  • Eiji Takimoto
    • 1
  • Kiyohito Nagano
    • 2
  1. 1.Department of InformaticsKyushu UniversityJapan
  2. 2.University of TokyoJapan

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