We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible parallel optimization for large-scale problems. Our method shares the efficiency and flexibility of block coordinate descent methods with the simplicity of primal-dual methods and utilizing the structure of the separable convex-concave saddle point problem. It is capable of solving a wide range of machine learning applications, including robust principal component analysis, Lasso, and feature selection by group Lasso, etc. Theoretically and empirically, we demonstrate significantly better performance than state-of-the-art methods in all these applications.

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible parallel optimization for large-scale problems. Our method shares the efficiency and flexibility of block coordinate descent methods with the simplicity of primal-dual methods and utilizing the structure of the separable convex-concave saddle point problem. It is capable of solving a wide range of machine learning applications, including robust principal component analysis, Lasso, and feature selection by group Lasso, etc. Theoretically and empirically, we demonstrate significantly better performance than state-of-the-art methods in all these applications.

We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle point problems, and incorporate stochastic block coordinate descent with adaptive stepsize into this framework. We theoretically show that our proposal of adaptive stepsize potentially achieves a sharper linear convergence rate compared with the existing methods. Additionally, since we can select "mini-batch" of block coordinates to update, our method is also amenable to parallel processing for large-scale data. We apply the proposed method to regularized empirical risk minimization and show that it performs comparably or, more often, better than state-of-the-art methods on both synthetic and real-world data sets.