Zhu Z., Storkey A.J. (2015) Adaptive Stochastic Primal-Dual Coordinate Descent for Separable Saddle Point Problems. In: Appice A., Rodrigues P., Santos Costa V., Soares C., Gama J., Jorge A. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2015. Lecture Notes in Computer Science, vol 9284. Springer, Cham
We consider a generic convex-concave saddle point problem with a 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 stepsizes into this framework. We theoretically show that our proposal of adaptive stepsizes 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.