Projection-Free Algorithms in Statistical Estimation
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Frank-Wolfe algorithm (FW) and its variants have gained a surge of interests in machine learning community due to its projection-free property. Recently people have reduced the gradient evaluation complexity of FW algorithm to (1/ϵ) for the smooth and strongly convex objective. This complexity result is especially significant in learning problem, as the overwhelming data size makes a single evluation of gradient computational expensive. However, in high-dimensional statistical estimation problems, the objective is typically not strongly convex, and sometimes even non-convex. In this paper, we extend the state-of-the-art FW type algorithms for the large-scale, high-dimensional estimation problem. We show that as long as the objective satisfies restricted strong convexity, and we are not optimizing over statistical limit of the model, the (1/ϵ) gradient evaluation complexity could still be attained.
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