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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.02638 |
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| _version_ | 1866913341419552768 |
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| author | Zhu, Zehan Huang, Yan Wang, Xin Xu, Jinming |
| author_facet | Zhu, Zehan Huang, Yan Wang, Xin Xu, Jinming |
| contents | In this paper, we propose a differentially private decentralized learning method (termed PrivSGP-VR) which employs stochastic gradient push with variance reduction and guarantees $(ε, δ)$-differential privacy (DP) for each node. Our theoretical analysis shows that, under DP Gaussian noise with constant variance, PrivSGP-VR achieves a sub-linear convergence rate of $\mathcal{O}(1/\sqrt{nK})$, where $n$ and $K$ are the number of nodes and iterations, respectively, which is independent of stochastic gradient variance, and achieves a linear speedup with respect to $n$. Leveraging the moments accountant method, we further derive an optimal $K$ to maximize the model utility under certain privacy budget in decentralized settings. With this optimized $K$, PrivSGP-VR achieves a tight utility bound of $\mathcal{O}\left( \sqrt{d\log \left( \frac{1}δ \right)}/(\sqrt{n}Jε) \right)$, where $J$ and $d$ are the number of local samples and the dimension of decision variable, respectively, which matches that of the server-client distributed counterparts, and exhibits an extra factor of $1/\sqrt{n}$ improvement compared to that of the existing decentralized counterparts, such as A(DP)$^2$SGD. Extensive experiments corroborate our theoretical findings, especially in terms of the maximized utility with optimized $K$, in fully decentralized settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02638 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | PrivSGP-VR: Differentially Private Variance-Reduced Stochastic Gradient Push with Tight Utility Bounds Zhu, Zehan Huang, Yan Wang, Xin Xu, Jinming Machine Learning In this paper, we propose a differentially private decentralized learning method (termed PrivSGP-VR) which employs stochastic gradient push with variance reduction and guarantees $(ε, δ)$-differential privacy (DP) for each node. Our theoretical analysis shows that, under DP Gaussian noise with constant variance, PrivSGP-VR achieves a sub-linear convergence rate of $\mathcal{O}(1/\sqrt{nK})$, where $n$ and $K$ are the number of nodes and iterations, respectively, which is independent of stochastic gradient variance, and achieves a linear speedup with respect to $n$. Leveraging the moments accountant method, we further derive an optimal $K$ to maximize the model utility under certain privacy budget in decentralized settings. With this optimized $K$, PrivSGP-VR achieves a tight utility bound of $\mathcal{O}\left( \sqrt{d\log \left( \frac{1}δ \right)}/(\sqrt{n}Jε) \right)$, where $J$ and $d$ are the number of local samples and the dimension of decision variable, respectively, which matches that of the server-client distributed counterparts, and exhibits an extra factor of $1/\sqrt{n}$ improvement compared to that of the existing decentralized counterparts, such as A(DP)$^2$SGD. Extensive experiments corroborate our theoretical findings, especially in terms of the maximized utility with optimized $K$, in fully decentralized settings. |
| title | PrivSGP-VR: Differentially Private Variance-Reduced Stochastic Gradient Push with Tight Utility Bounds |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2405.02638 |