A Stochastic Trust Region Method for Non-convex Minimization

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 O(1/k2/3) 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, √ε)-approximate local minimum within O(√n/ε1.5) stochastic Hessian oracle queries. This improves state-of-the-art result by O(n1/6). Experiments verify theoretical conclusions and the efficiency of STR.