The Common-directions Method for Regularized Empirical Risk Minimization

Po-Wei Wang, Ching-Pei Lee, Chih-Jen Lin

Abstract: State-of-the-art first- and second-order optimization methods are able to achieve either fast global linear convergence rates or quadratic convergence, but not both of them. In this work, we propose an interpolation between first- and second-order methods for regularized empirical risk minimization that exploits the problem structure to efficiently combine multiple update directions. Our method attains both optimal global linear convergence rate for first-order methods, and local quadratic convergence. Experimental results show that our method outperforms state-of-the-art first- and second-order optimization methods in terms of the number of data accesses, while is competitive in training time.