  In this work, we study data preconditioning, a well-known and long-existing
technique, for boosting the convergence of first-order methods for regularized
loss minimization. It is well understood that the condition number of the
problem, i.e., the ratio of the Lipschitz constant to the strong convexity
modulus, has a harsh effect on the convergence of the first-order optimization
methods. Therefore, minimizing a small regularized loss for achieving good
generalization performance, yielding an ill conditioned problem, becomes the
bottleneck for big data problems. We provide a theory on data preconditioning
for regularized loss minimization. In particular, our analysis exhibits an
appropriate data preconditioner and characterizes the conditions on the loss
function and on the data under which data preconditioning can reduce the
condition number and therefore boost the convergence for minimizing the
regularized loss. To make the data preconditioning practically useful, we
endeavor to employ and analyze a random sampling approach to efficiently
compute the preconditioned data. The preliminary experiments validate our
theory.
