Learning Set Functions with Limited Complementarity

Abstract

We study PMAC-learning of real-valued set functions with limited complementarity. We prove, to our knowledge, the first nontrivial learnability result for set functions exhibiting complementarity, generalizing Balcan and Harvey’s result for submodular functions. We prove a nearly matching information theoretical lower bound on the number of samples required, complementing our learnability result. We conduct numerical simulations to show that our algorithm is likely to perform well in practice.