A Stochastic Trust Region Method for Non-convex Minimization - Shen, Zebang; Zhou, Pan; Fang, Cong; Ribeiro, Alejandro (2019)
We target the problem of finding a local minimum in non-convex finite-sum minimization. Towards this goal, we first prove that the trust region method with inexact gradient and Hessian estimation can achieve a convergence rate of order$\mathcal{O}(1/{k^{2/3}})$as long as those differential estimations are sufficiently accurate. Combining such result with a novel Hessian estimator, we propose the sample-efficient stochastic trust region (STR) algorithm which finds an$(ε, \sqrt{ε})$ -approximate local minimum within$\mathcal{O}({\sqrt{n}}/{ε^{1.5}})$stochastic Hessian oracle queries. This improves state-of-the-art result by$\mathcal{O}(n^{1/6})$ . Experiments verify theoretical conclusions and the efficiency of STR.