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 (, ²/2) -R\'enyi differential privacy and finds a (, ) -stationary point so long as M= (d³ + d^3/2²). 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 d.