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Regularized empirical risk minimization problem with linear predictor appearsfrequently in machine learning. In this paper, we propose a new stochasticprimal-dual method to solve this class of problems. Different from existingmethods, our proposed methods only require O(1) operations in each iteration.We also develop a variance-reduction variant of the algorithm that convergeslinearly. Numerical experiments suggest that our methods are faster thanexisting ones such as proximal SGD, SVRG and SAGA on high-dimensional problems.

Stochastic Primal-Dual Method for Empirical Risk Minimization with $\mathcal{O}(1)$ Per-Iteration Complexity