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

A Stronger Convergence Result on the Proximal Incremental Aggregated Gradient Method