Private Zeroth-Order Nonsmooth Nonconvex Optimization

Fuente: arXiv
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Main Authors: Zhang, Qinzi, Tran, Hoang, Cutkosky, Ashok
Format: Preprint
Published: 2024
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author Zhang, Qinzi
Tran, Hoang
Cutkosky, Ashok
author_facet Zhang, Qinzi
Tran, Hoang
Cutkosky, Ashok
contents 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 $ρ\ge \sqrt{d}ε$.
format Preprint
id arxiv_https___arxiv_org_abs_2406_19579
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Private Zeroth-Order Nonsmooth Nonconvex Optimization
Zhang, Qinzi
Tran, Hoang
Cutkosky, Ashok
Optimization and Control
Cryptography and Security
Machine Learning
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 $ρ\ge \sqrt{d}ε$.
title Private Zeroth-Order Nonsmooth Nonconvex Optimization
topic Optimization and Control
Cryptography and Security
Machine Learning
url https://arxiv.org/abs/2406.19579