Fast Semidifferential-based Submodular Function Optimization
This work addresses submodular optimization problems, which are widely applicable in machine learning, by providing a unifying and practical framework, though it appears incremental as it builds on and generalizes prior methods.
The authors tackled submodular function optimization by introducing a framework based on discrete semidifferentials, which unifies minimization and maximization approaches and generalizes many existing methods, with empirical experiments supporting the theoretical analysis.
We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute and then efficiently optimize submodular semigradients, offer new and generalize many old methods for submodular optimization. Our approach, moreover, takes steps towards providing a unifying paradigm applicable to both submodular min- imization 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.