Research map / Optimization / Nonconvex and smooth optimization
Linear Convergence of a Frank-Wolfe Type Algorithm over Trace-Norm Balls
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace Frank-Wolfe's rank-1 update with a rank-k update | Trace-norm-ball optimization with smooth, strongly convex objectives and rank(X*) ≤ k · Trace-norm ball | iterations to ε-approximation: O(β/ε) -> O(β/α log 1/ε) | Helped |
| Use k-SVD instead of 1-SVD in the update | blockFW · Trace-norm ball; rank(X*) ≤ k | 1-SVD computations to ε-approximation: O(β/ε) -> O(kβ/α log 1/ε) | Helped |
| Apply blockFW when the trace-norm bound is small and the optimum is low-rank | Matrix completion and polynomial neural-network experiments · MOVIELENS1M matrix completion; MNIST polynomial neural network | number of 1-SVD computations | Helped |
| Apply blockFW when the trace-norm bound is large and the optimum has higher rank | Matrix completion and polynomial neural-network experiments · MOVIELENS and MNIST | number of 1-SVD computations | No clear effect |
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