On the Convergence Rate of Decomposable Submodular Function Minimization [article]

Robert Nishihara, Stefanie Jegelka, Michael I. Jordan
2014 arXiv   pre-print
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an easy-to-use, parallelizable algorithm for minimizing submodular functions that decompose as the sum of "simple" submodular functions. Empirically, this algorithm performs extremely well, but no theoretical analysis was given. In this paper, we show that the algorithm
more » ... onverges linearly, and we provide upper and lower bounds on the rate of convergence. Our proof relies on the geometry of submodular polyhedra and draws on results from spectral graph theory.
arXiv:1406.6474v3 fatcat:ufg3lx3tsnhbhinuybhnzge3ye