Improved algorithms for non-submodular function maximization problem

Abstract

The concept of submodularity finds wide applications in data science, artificial intelligence, and machine learning, providing a boost to the investigation of new ideas, innovative techniques, and creative algorithms to solve different submodular optimization problems arising from a diversity of applications. However pure submodular or supermodular problems only represent a small portion of the problems we are facing in real life applications. The main focus of this work is to consider a non-submodular function maximization problem subject to a cardinality constraint, where the objective function is the sum of a monotone γ-weakly submodular function and a supermodular function. This problem includes some previously studied problems as special cases, such as the submodular+supermodular maximization problem when γ=1, and the γ-weakly submodular function maximization problem when the supermodular function is void. We present greedy algorithms for this generalized problem under both offline and streaming models, improving existing results.