Stochastic Parallel Block Coordinate Descent for Large-scale Saddle Point Problems
This provides an efficient parallel optimization method for large-scale machine learning problems, though it appears incremental as it combines existing techniques.
The authors tackled large-scale convex-concave saddle point problems with separable structures by proposing a stochastic parallel block coordinate descent method with adaptive primal-dual updates. They demonstrated significantly better performance than state-of-the-art methods across applications like robust PCA, Lasso, and group Lasso.
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.