Distributed Nonconvex Optimization with Double Privacy Protection and Exact Convergence
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917058017492992 |
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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 |