Title: A Deterministic Nonsmooth Frank Wolfe Algorithm with Coreset Guarantees,
Abstract: We present a new Frank-Wolfe (FW) type algorithm that is applicable to
minimization problems with a nonsmooth convex objective. We provide convergence
bounds and show that the scheme yields so-called coreset results for various
Machine Learning problems including 1-median, Balanced Development, Sparse PCA,
Graph Cuts, and the $\ell_1$-norm-regularized Support Vector Machine (SVM)
among others. This means that the algorithm provides approximate solutions to
these problems in time complexity bounds that are not dependent on the size of
the input problem. Our framework, motivated by a growing body of work on
sublinear algorithms for various data analysis problems, is entirely
deterministic and makes no use of smoothing or proximal operators. Apart from
these theoretical results, we show experimentally that the algorithm is very
practical and in some cases also offers significant computational advantages on
large problem instances. We provide an open source implementation that can be
adapted for other problems that fit the overall structure.