CCCP is Frank-Wolfe in disguise

Alp Yurtsever · Suvrit Sra

Hall J #935

Keywords: [ sinkhorn ] [ conditional gradient method ] [ difference of convex programming ] [ expectation maximization ] [ cccp ] [ frank-wolfe ] [ convex-concave procedure ]


This paper uncovers a simple but rather surprising connection: it shows that the well-known convex-concave procedure (CCCP) and its generalization to constrained problems are both special cases of the Frank-Wolfe (FW) method. This connection not only provides insight of deep (in our opinion) pedagogical value, but also transfers the recently discovered convergence theory of nonconvex Frank-Wolfe methods immediately to CCCP, closing a long-standing gap in its non-asymptotic convergence theory. We hope the viewpoint uncovered by this paper spurs the transfer of other advances made for FW to both CCCP and its generalizations.

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