We study the problem of approximating stationary points of Lipschitz and smooth functions under (ε,δ)-differential privacy (DP) in both the finite-sum and stochastic settings. A point w is called an α-stationary point of a function F:ℝ^d→ℝ if ∇ F(w)≤α. We give a new construction that improves over the existing rates in the stochastic optimization setting, where the goal is to find approximate stationary points of the population risk given n samples. Our construction finds a Õ(1/n^1/3 + [√(d)/nε]…