We lower bound the complexity of finding $$\epsilon $$ -stationary points (with gradient norm at most ) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions through queries to an unbiased oracle with bounded variance, we prove that (in worst case) any algorithm requires least ^{-4}$$ find point. The is tight, and establis...

A stochastic version of the branch and bound method is proposed for solving stochastic global optimization problems. The method, instead of deterministic bounds, uses stochastic upper and lower estimates of the optimal value of subproblems, to guide the partitioning process. Almost sure convergence of the method is proved and random accuracy estimates derived. Methods for constructing random bo...