Boosting Frank-Wolfe by Chasing Gradients
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The Frank-Wolfe algorithm has become a popular first-order optimization algorithm for it is simple and projection-free, and it has been successfully applied to a variety of real-world problems. Its main drawback however lies in its convergence rate, which can be excessively slow due to naive descent directions. We propose to speed-up the Frank-Wolfe algorithm by better aligning the descent direction with that of the negative gradient via a subroutine. This subroutine chases the negative gradient direction in a matching pursuit-style while still preserving the projection-free property. Although the approach is reasonably natural, it produces very significant results. We derive convergence rates O(1/t) to O(e^-ω t^p) of our method where p∈]0,1], and we demonstrate its competitive advantage both per iteration and in CPU time over the state-of-the-art in a series of computational experiments.
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