Budget-Conditioned Clipping Policies for Differentially Private Federated Learning

Gradient clipping is a central but brittle design choice in differentially private federated learning: overly small thresholds bias client updates, whereas overly large thresholds amplify the noise required by privacy. This trade-off is further complicated by client heterogeneity and personalized privacy budgets, where a single global threshold is often mismatched and online adaptation from private training statistics can complicate privacy accounting. We study clipping-threshold selection as a privacy-budget-conditioned policy learning problem. We propose PAC-DP, a proxy-learned clipping framework for record-level locally private federated learning. Before private training, PAC-DP calibrates a deterministic policy $\pi_\theta(\varepsilon,t)$ from public or synthetic proxy simulations, mapping a client's target privacy budget and the training round to a clipping threshold. The policy is then frozen and used during private training, so deployed thresholds depend only on the declared budget, round index, and public/proxy-learned parameters, not on private gradients, losses, or client-specific update histories. PAC-DP combines this policy with per-example clipping, Gaussian perturbation, and per-client RDP accounting. We show that, under public or separately privatized proxy calibration, the frozen policy introduces no additional record-level privacy loss beyond the clipped Gaussian mechanisms. We further analyze the clipping-sensitive utility trade-off through a decomposition involving clipping bias, stochastic variance, client heterogeneity, and DP noise, and characterize proxy-to-target transfer via a regret bound. Experiments on MNIST, CIFAR-10, CIFAR-100, and Heart Disease show that PAC-DP improves the privacy--utility trade-off and communication efficiency over implemented fixed-threshold and adaptive DP-FL baselines under matched privacy budgets.