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Linear Convergence of a Frank-Wolfe Type Algorithm over Trace-Norm Balls
We propose a rank- variant of the classical Frank-Wolfe algorithm to solve
convex optimization over a trace-norm ball. Our algorithm replaces the top
singular-vector computation (-SVD) in Frank-Wolfe with a top-
singular-vector computation (-SVD), which can be done by repeatedly applying
-SVD times. Alternatively, our algorithm can be viewed as a rank-
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 . This improves
the convergence rate and the total time complexity of the Frank-Wolfe method
and its variants.Comment: In NIPS 201
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