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Linear Convergence of a Frank-Wolfe Type Algorithm over Trace-Norm Balls

Author(s): Allen-Zhu, Zeyuan; Hazan, Elad; Hu, Wei; Li, Yuanzhi

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Abstract: We propose a rank-k variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball. Our algorithm replaces the top singular-vector computation (1-SVD) in Frank-Wolfe with a top-k singular-vector computation (k-SVD), which can be done by repeatedly applying 1-SVD k times. Alternatively, our algorithm can be viewed as a rank-k restricted version of projected gradient descent. We show that our algorithm has a linear convergence rate when the objective function is smooth and strongly convex, and the optimal solution has rank at most k. This improves the convergence rate and the total time complexity of the Frank-Wolfe method and its variants.
Publication Date: 2017
Citation: Allen-Zhu, Zeyuan, Elad Hazan, Wei Hu, and Yuanzhi Li. "Linear Convergence of a Frank-Wolfe Type Algorithm over Trace-Norm Balls." Advances in Neural Information Processing Systems 30 (2017).
ISSN: 1049-5258
Type of Material: Conference Article
Journal/Proceeding Title: Advances in Neural Information Processing Systems
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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