Private Zeroth-Order Nonsmooth Nonconvex Optimization
Qinzi Zhang, Hoang Tran, Ashok Cutkosky
6/27/2024
math.OCcs.CRcs.LG
No confident code implementation found for this paper.
Abstract
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 $(α,αρ^2/2)$-Rényi differential privacy and finds a $(δ,ε)$-stationary point so long as $M=\tildeΩ\left(\frac{d}{δε^3} + \frac{d^{3/2}}{ρδε^2}\right)$. 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 $ρ\ge \sqrt{d}ε$.
