  We consider the problem of minimizing the sum of two convex functions: one is
smooth and given by a gradient oracle, and the other is separable over blocks
of coordinates and has a simple known structure over each block. We develop an
accelerated randomized proximal coordinate gradient (APCG) method for
minimizing such convex composite functions. For strongly convex functions, our
method achieves faster linear convergence rates than existing randomized
proximal coordinate gradient methods. Without strong convexity, our method
enjoys accelerated sublinear convergence rates. We show how to apply the APCG
method to solve the regularized empirical risk minimization (ERM) problem, and
devise efficient implementations that avoid full-dimensional vector operations.
For ill-conditioned ERM problems, our method obtains improved convergence rates
than the state-of-the-art stochastic dual coordinate ascent (SDCA) method.
