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Minimizing the difference of two submodular (DS) functions is a problem thatnaturally occurs in various machine learning problems. Although it is wellknown that a DS problem can be equivalently formulated as the minimization ofthe difference of two convex (DC) functions, existing algorithms do not fullyexploit this connection. A classical algorithm for DC problems is called the DCalgorithm (DCA). We introduce variants of DCA and its complete form (CDCA) thatwe apply to the DC program corresponding to DS minimization. We extend existingconvergence properties of DCA, and connect them to convergence properties onthe DS problem. Our results on DCA match the theoretical guarantees satisfiedby existing DS algorithms, while providing a more complete characterization ofconvergence properties. In the case of CDCA, we obtain a stronger localminimality guarantee. Our numerical results show that our proposed algorithmsoutperform existing baselines on two applications: speech corpus selection andfeature selection.

Difference of Submodular Minimization via DC Programming