Learning submodular functions

Abstract

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. © 2012 Springer-Verlag.