Fast semidifferential-based submodular function optimization

We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidi fferentials (sub- and super-di fferentials). The resulting algorithms, which repeatedly compute and then efficiently optimize submodular semigradients, o ver new and generalize many old methods for submodular optimization. Our approach, moreover, takes steps towards providing a unifying paradigm applicable to both submodular minimization and maximization, problems that historically have been treated quite distinctly. The practicality of our algorithms is important since interest in submodularity, owing to its natural and wide applicability, has recently been in ascendance within machine learning. We analyze theoretical properties of our algorithms for minimization and maximization, and show that many state-of-the-art maximization algorithms are special cases. Lastly, we complement our theoretical analyses with supporting empirical experiments.
Authors: Rishabh Iyer, Stefanie Jegelka, Jeff Bilmes
Publication Date: June 2013
Conference: International Conference on Machine Learning (ICML)