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On the Convergence Rate of Decomposable Submodular Function Minimization
Robert Nishihara · Stefanie Jegelka · Michael Jordan

Mon Dec 08 04:00 PM -- 08:59 PM (PST) @ Level 2, room 210D

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 converges 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.

Author Information

Robert Nishihara (Anyscale)
Stefanie Jegelka (MIT)
Michael Jordan (UC Berkeley)

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