A Dual Augmented Block Minimization Framework for Learning with Limited Memory

In past few years, several techniques have been proposed for training of linear Support Vector Machine (SVM) in limited-memory setting, where a dual block-coordinate descent (dual-BCD) method was used to balance cost spent on I/O and computation. In this paper, we consider the more general setting of regularized \emph{Empirical Risk Minimization (ERM)} when data cannot fit into memory. In particular, we generalize the existing block minimization framework based on strong duality and \emph{Augmented Lagrangian} technique to achieve global convergence for ERM with arbitrary convex loss function and regularizer. The block minimization framework is flexible in the sense that, given a solver working under sufficient memory, one can integrate it with the framework to obtain a solver globally convergent under limited-memory condition. We conduct experiments on L1-regularized classification and regression problems to corroborate our convergence theory and compare the proposed framework to algorithms adopted from online and distributed settings, which shows superiority of the proposed approach on data of size ten times larger than the memory capacity.