Online prediction under submodular constraints

Authors:
Daiki Suehiro;Kohei Hatano;Shuji Kijima;Eiji Takimoto;Kiyohito Nagano
Affiliations:
Department of Informatics, Kyushu University, Japan;Department of Informatics, Kyushu University, Japan;Department of Informatics, Kyushu University, Japan;Department of Informatics, Kyushu University, Japan;University of Tokyo, Japan
Venue:
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
Year:
2012

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Abstract

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(n2)-time algorithms.