Convergent Differential Privacy Analysis for General Federated Learning: the $f$-DP Perspective

• URL: http://arxiv.org/abs/2408.15621v2
• Date: Sat, 12 Oct 2024 08:27:49 GMT
• Title: Convergent Differential Privacy Analysis for General Federated Learning: the $f$-DP Perspective
• Authors: Yan Sun, Li Shen, Dacheng Tao,
• Abstract summary: Federated learning (FL) is an efficient collaborative training paradigm with a focus on local privacy. differential privacy (DP) is a classical approach to capture and ensure the reliability of private protections.
• Score: 57.35402286842029
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Federated learning (FL) is an efficient collaborative training paradigm extensively developed with a focus on local privacy, and differential privacy (DP) is a classical approach to capture and ensure the reliability of private security. Their powerful cooperation provides a promising paradigm for the large-scale private clients. As a predominant implementation, the noisy perturbation has been widely studied, being theoretically proven to offer significant protections. 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. 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. $(\epsilon,\delta)$-DP and R$\acute{\text{e}}$nyi-DP (RDP).

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