Convergent Differential Privacy Analysis for General Federated Learning
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909038554382336 |
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| author | Sun, Yan Zhang, Qixin Shen, Li Tao, Dacheng |
| author_facet | Sun, Yan Zhang, Qixin Shen, Li Tao, Dacheng |
| contents | The powerful cooperation of federated learning (FL) and differential privacy~(DP) provides a promising paradigm for the large-scale private clients. However, existing analyses in FL-DP mostly rely on the composition theorem and cannot tightly quantify the privacy leakage challenges, which is tight for a few communication rounds but yields an arbitrarily loose and divergent bound eventually. This also implies a counterintuitive judgment, suggesting that FL-DP may not provide adequate privacy support during long-term training under constant-level noisy perturbations, yielding discrepancy between the theoretical and experimental results. To further investigate the convergent privacy and reliability of the FL-DP framework, in this paper, we comprehensively evaluate the worst privacy of two classical methods under the non-convex and smooth objectives based on the $f$-DP analysis. With the aid of the shifted interpolation technique, we successfully prove that privacy in {\ttfamily Noisy-FedAvg} has a tight convergent bound. Moreover, with the regularization of the proxy term, privacy in {\ttfamily Noisy-FedProx} has a stable constant lower bound. Our analysis further demonstrates a solid theoretical foundation for the reliability of privacy in FL-DP. Meanwhile, our conclusions can also be losslessly converted to other classical DP analytical frameworks, e.g. $(ε,δ)$-DP and R$\acute{\text{e}}$nyi-DP~(RDP), to provide more fine-grained understandings for the FL-DP frameworks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_15621 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergent Differential Privacy Analysis for General Federated Learning Sun, Yan Zhang, Qixin Shen, Li Tao, Dacheng Machine Learning Cryptography and Security The powerful cooperation of federated learning (FL) and differential privacy~(DP) provides a promising paradigm for the large-scale private clients. However, existing analyses in FL-DP mostly rely on the composition theorem and cannot tightly quantify the privacy leakage challenges, which is tight for a few communication rounds but yields an arbitrarily loose and divergent bound eventually. This also implies a counterintuitive judgment, suggesting that FL-DP may not provide adequate privacy support during long-term training under constant-level noisy perturbations, yielding discrepancy between the theoretical and experimental results. To further investigate the convergent privacy and reliability of the FL-DP framework, in this paper, we comprehensively evaluate the worst privacy of two classical methods under the non-convex and smooth objectives based on the $f$-DP analysis. With the aid of the shifted interpolation technique, we successfully prove that privacy in {\ttfamily Noisy-FedAvg} has a tight convergent bound. Moreover, with the regularization of the proxy term, privacy in {\ttfamily Noisy-FedProx} has a stable constant lower bound. Our analysis further demonstrates a solid theoretical foundation for the reliability of privacy in FL-DP. Meanwhile, our conclusions can also be losslessly converted to other classical DP analytical frameworks, e.g. $(ε,δ)$-DP and R$\acute{\text{e}}$nyi-DP~(RDP), to provide more fine-grained understandings for the FL-DP frameworks. |
| title | Convergent Differential Privacy Analysis for General Federated Learning |
| topic | Machine Learning Cryptography and Security |
| url | https://arxiv.org/abs/2408.15621 |