Primal-Dual Block Frank-Wolfe
This addresses computational efficiency for machine learning practitioners working on sparse/low-rank optimization problems like Elastic Net and SVMs, though it appears incremental as a variant of an existing algorithm.
The authors tackled optimization problems with sparse/low-rank structure by proposing a variant of the Frank-Wolfe algorithm that reduces per-iteration cost while maintaining linear convergence, empirically showing it outperforms state-of-the-art methods on classification tasks.
We propose a variant of the Frank-Wolfe algorithm for solving a class of sparse/low-rank optimization problems. Our formulation includes Elastic Net, regularized SVMs and phase retrieval as special cases. The proposed Primal-Dual Block Frank-Wolfe algorithm reduces the per-iteration cost while maintaining linear convergence rate. The per iteration cost of our method depends on the structural complexity of the solution (i.e. sparsity/low-rank) instead of the ambient dimension. We empirically show that our algorithm outperforms the state-of-the-art methods on (multi-class) classification tasks.