  We study the convergence rate of the proximal incremental aggregated gradient
(PIAG) method for minimizing the sum of a large number of smooth component
functions (where the sum is strongly convex) and a non-smooth convex function.
At each iteration, the PIAG method moves along an aggregated gradient formed by
incrementally updating gradients of component functions at least once in the
last $K$ iterations and takes a proximal step with respect to the non-smooth
function. We show that the PIAG algorithm attains an iteration complexity that
grows linear in the condition number of the problem and the delay parameter
$K$. This improves upon the previously best known global linear convergence
rate of the PIAG algorithm in the literature which has a quadratic dependence
on $K$.
