Differential privacy (DP) is crucial for safeguarding sensitive client information in federated learning (FL), yet traditional DP-FL methods rely predominantly on fixed gradient clipping thresholds. Such static clipping neglects significant client heterogeneity and varying privacy sensitivities, which may lead to an unfavorable privacy-utility trade-off. In this paper, we propose PAC-DP, a Personalized Adaptive Clipping framework for federated learning under record-level local differential privacy. PAC-DP introduces a Simulation-CurveFitting approach leveraging a server-hosted public proxy dataset to learn an effective mapping between personalized privacy budgets epsilon and gradient clipping thresholds C, which is then deployed online with a lightweight round-wise schedule. This design enables budget-conditioned threshold selection while avoiding data-dependent tuning during training. We provide theoretical analyses establishing convergence guarantees under the per-example clipping and Gaussian perturbation mechanism and a reproducible privacy accounting procedure. Extensive evaluations on multiple FL benchmarks show that PAC-DP surpasses conventional fixed-threshold approaches under matched privacy budgets, improving accuracy by up to 26% and accelerating convergence by up to 45.5% in our evaluated settings.

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