Random Coordinate Descent Methods for Minimizing Decomposable Submodular Functions
This work provides a more efficient solution for large-scale submodular function minimization in machine learning and computer vision, though it is incremental as it builds on convex optimization techniques.
The paper tackles the problem of minimizing decomposable submodular functions, which is computationally expensive for large-scale applications, by introducing random coordinate descent methods that achieve faster linear convergence rates and lower iteration costs compared to existing approaches like alternating projection methods.
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have high running times and are unsuitable for large-scale problems. Recent work have used convex optimization techniques to obtain very practical algorithms for minimizing functions that are sums of ``simple" functions. In this paper, we use random coordinate descent methods to obtain algorithms with faster linear convergence rates and cheaper iteration costs. Compared to alternating projection methods, our algorithms do not rely on full-dimensional vector operations and they converge in significantly fewer iterations.