Distributed Nonconvex Optimization with Double Privacy Protection and Exact Convergence

Fuente: arXiv
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Hauptverfasser: Ou, Zichong, Wang, Dandan, Liu, Zixuan, Lu, Jie
Format: Preprint
Veröffentlicht: 2025
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author Ou, Zichong
Wang, Dandan
Liu, Zixuan
Lu, Jie
author_facet Ou, Zichong
Wang, Dandan
Liu, Zixuan
Lu, Jie
contents Motivated by the pervasive lack of privacy protection in existing distributed nonconvex optimization methods, this paper proposes a decentralized proximal primal-dual algorithm enabling double protection of privacy ($\text{DPP}^2$) for minimizing nonconvex sum-utility functions over multi-agent networks, which ensures zero leakage of critical local information during inter-agent communications. We develop a two-tier privacy protection mechanism that first merges the primal and dual variables by means of a variable transformation, followed by embedding an additional random perturbation to further obfuscate the transmitted information. We theoretically establish that $\text{DPP}^2$ ensures differential privacy for local objectives while achieving exact convergence under nonconvex settings. Specifically, $\text{DPP}^2$ converges sublinearly to a stationary point and attains a linear convergence rate under the additional Polyak-Łojasiewicz (P-Ł) condition. Finally, a numerical example demonstrates the superiority of $\text{DPP}^2$ over a number of state-of-the-art algorithms, showcasing the faster, exact convergence achieved by $\text{DPP}^2$ under the same level of differential privacy.
format Preprint
id arxiv_https___arxiv_org_abs_2511_02283
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Distributed Nonconvex Optimization with Double Privacy Protection and Exact Convergence
Ou, Zichong
Wang, Dandan
Liu, Zixuan
Lu, Jie
Optimization and Control
Motivated by the pervasive lack of privacy protection in existing distributed nonconvex optimization methods, this paper proposes a decentralized proximal primal-dual algorithm enabling double protection of privacy ($\text{DPP}^2$) for minimizing nonconvex sum-utility functions over multi-agent networks, which ensures zero leakage of critical local information during inter-agent communications. We develop a two-tier privacy protection mechanism that first merges the primal and dual variables by means of a variable transformation, followed by embedding an additional random perturbation to further obfuscate the transmitted information. We theoretically establish that $\text{DPP}^2$ ensures differential privacy for local objectives while achieving exact convergence under nonconvex settings. Specifically, $\text{DPP}^2$ converges sublinearly to a stationary point and attains a linear convergence rate under the additional Polyak-Łojasiewicz (P-Ł) condition. Finally, a numerical example demonstrates the superiority of $\text{DPP}^2$ over a number of state-of-the-art algorithms, showcasing the faster, exact convergence achieved by $\text{DPP}^2$ under the same level of differential privacy.
title Distributed Nonconvex Optimization with Double Privacy Protection and Exact Convergence
topic Optimization and Control
url https://arxiv.org/abs/2511.02283