Before revision:  First, we present a stochastic method for non-convex SBO with only one lower problem and establish its sample complexity of O(1/\epsilon^3) for finding an \epsilon-stationary point under appropriate conditions , matching the lower bound for stochastic smooth non-convex optimization.
After revision:  First, we present a stochastic method for non-convex SBO with only one lower problem and establish its sample complexity of O(1/\epsilon^3) for finding an \epsilon-stationary point under Lipschitz continuous conditions of stochastic oracles , matching the lower bound for stochastic smooth non-convex optimization.