An Adaptive Sample Size Trust-Region Method for Finite-Sum Minimization

We propose a trust-region method for finite-sum minimization with an adaptive sample size adjustment technique, which is practical in the sense that it leads to a globally convergent method that shows strong performance empirically without the need for experimentation by the user. During the optimization process, the size of the samples is adaptively increased (or decreased) depending on the progress made on the objective function. We prove that after a finite number iterations the sample includes all points from the data set and the method becomes a full-batch trust-region method. Numerical experiments on convex and nonconvex problems support our claim that our algorithm has significant advantages compared to current state-of-the-art methods.