FrankWolfe with Subsampling Oracle
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:25912600, 2018.
Abstract
We analyze two novel randomized variants of the FrankWolfe (FW) or conditional gradient algorithm. While classical FW algorithms require solving a linear minimization problem over the domain at each iteration, the proposed method only requires to solve a linear minimization problem over a small subset of the original domain. The first algorithm that we propose is a randomized variant of the original FW algorithm and achieves a $\mathcal{O}(1/t)$ sublinear convergence rate as in the deterministic counterpart. The second algorithm is a randomized variant of the Awaystep FW algorithm, and again as its deterministic counterpart, reaches linear (i.e., exponential) convergence rate making it the first provably convergent randomized variant of Awaystep FW. In both cases, while subsampling reduces the convergence rate by a constant factor, the linear minimization step can be a fraction of the cost of that of the deterministic versions, especially when the data is streamed. We illustrate computational gains of both algorithms on regression problems, involving both $\ell_1$ and latent group lasso penalties.
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