Doubly Greedy Primal-Dual Coordinate Descent for Sparse Empirical Risk Minimization

We consider the popular problem of sparse empirical risk minimization with linear predictors and a large number of both features and observations. With a convex-concave saddle point objective reformulation, we propose a Doubly Greedy Primal-Dual 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 large-scale Multi-class data sets show that our algorithm achieves up to 30 times speedup on several state-of-the-art optimization methods.

PDF Abstract
No code implementations yet. Submit your code now



  Add Datasets introduced or used in this paper

Results from the Paper

  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.


No methods listed for this paper. Add relevant methods here