Revisiting Frank-Wolfe for Structured Nonconvex Optimization

• URL: http://arxiv.org/abs/2503.08921v1
• Date: Tue, 11 Mar 2025 22:09:44 GMT
• Title: Revisiting Frank-Wolfe for Structured Nonconvex Optimization
• Authors: Hoomaan Maskan, Yikun Hou, Suvrit Sra, Alp Yurtsever,
• Abstract summary: We introduce a new projection (Frank-Wolfe) method for optimizing structured non functions that are expressed as a difference of two convex functions.<n>We prove that the proposed method achieves in $O-(O-)$(O-)$(O-)$(O-)$(O-)$(O-)$(O-)$(O-)$(O-)$(O-)$(O-)$(O-)$(
• Score: 33.44652927142219
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a new projection-free (Frank-Wolfe) method for optimizing structured nonconvex functions that are expressed as a difference of two convex functions. This problem class subsumes smooth nonconvex minimization, positioning our method as a promising alternative to the classical Frank-Wolfe algorithm. DC decompositions are not unique; by carefully selecting a decomposition, we can better exploit the problem structure, improve computational efficiency, and adapt to the underlying problem geometry to find better local solutions. We prove that the proposed method achieves a first-order stationary point in $O(1/\epsilon^2)$ iterations, matching the complexity of the standard Frank-Wolfe algorithm for smooth nonconvex minimization in general. Specific decompositions can, for instance, yield a gradient-efficient variant that requires only $O(1/\epsilon)$ calls to the gradient oracle. Finally, we present numerical experiments demonstrating the effectiveness of the proposed method compared to the standard Frank-Wolfe algorithm.

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