Online prediction under submodular constraints

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(n 2)-time algorithms. © 2012 Springer-Verlag.