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Frank-Wolfe with Subsampling Oracle
Thomas Kerdreux · Fabian Pedregosa · Alexandre d'Aspremont

Fri Jul 13 09:15 AM -- 12:00 PM (PDT) @ Hall B #38
We analyze two novel randomized variants of the Frank-Wolfe (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 \emph{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 Away-step FW algorithm, and again as its deterministic counterpart, reaches linear (i.e., exponential) convergence rate making it the first provably convergent randomized variant of Away-step 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.

Author Information

Thomas Kerdreux (INRIA)
Fabian Pedregosa (UC Berkeley)
Alexandre d'Aspremont (CNRS, Ecole Normale Superieure)

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