Private Zeroth-Order Nonsmooth Nonconvex Optimization

We introduce a new zeroth-order algorithm for private stochastic optimization on nonconvex and nonsmooth objectives. Given a dataset of size M, our algorithm ensures (α,αρ²/2)-R\'enyi differential privacy and finds a (δ,ε)-stationary point so long as M=Ω(d/δε³ + d3/2ρδε²). This matches the optimal complexity of its non-private zeroth-order analog. Notably, although the objective is not smooth, we have privacy ``for free'' whenever ρ ≥ √dε.