Private Zeroth-Order Nonsmooth Nonconvex Optimization
<|reference_start|>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 $(\alpha,\alpha\rho^2/2)$-R\'enyi differential privacy and finds a $(\delta,\epsilon)$-stationary point so long as $M=\tilde\Omega\left(\frac{d}{\delta\epsilon^3} + \frac{d^{3/2}}{\rho\delta\epsilon^2}\right)$. 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 $\rho \ge \sqrt{d}\epsilon$.<|reference_end|>
@article{zhang2024private,
    title={Private Zeroth-Order Nonsmooth Nonconvex Optimization},
    author={Qinzi Zhang, Hoang Tran, Ashok Cutkosky},
    journal={arXiv preprint arXiv:2406.19579},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.19579},
    primaryClass={math.OC cs.CR cs.LG}
}