Doubly Greedy PrimalDual Coordinate Descent for Sparse Empirical Risk Minimization
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:20342042, 2017.
Abstract
We consider the popular problem of sparse empirical risk minimization with linear predictors and a large number of both features and observations. With a convexconcave saddle point objective reformulation, we propose a Doubly Greedy PrimalDual Coordinate Descent algorithm that is able to exploit sparsity in both primal and dual variables. It enjoys a low cost per iteration and our theoretical analysis shows that it converges linearly with a good iteration complexity, provided that the set of primal variables is sparse. We then extend this algorithm further to leverage active sets. The resulting new algorithm is even faster, and experiments on largescale Multiclass data sets show that our algorithm achieves up to 30 times speedup on several stateoftheart optimization methods.
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