A Stochastic Trust Region Algorithm Based on Careful Step Normalization

Abstract

An algorithm is proposed for solving stochastic and finite-sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within a specified interval. The complete algorithm—which dynamically chooses whether to employ normalized steps—is proved to have convergence guarantees that are similar to those possessed by a traditional stochastic gradient approach under various sets of conditions related to the accuracy of the stochastic gradient estimates and choice of step size sequence. The results of numerical experiments where the method is employed to minimize convex and nonconvex machine learning test problems are presented. These results illustrate that the method can outperform a traditional stochastic gradient approach.