SlaClip: Gradient Norm Slacks can be Indicator for Adaptive Clipping in DP-SGD

Abstract

Differentially private stochastic gradient descent (DP-SGD) achieves privacy by clipping per-sample gradients and injecting Gaussian noise, but its utility is highly sensitive to the choice of the clipping threshold $C$. A fixed $C$ often degrades performance and necessitates repeated empirical calibration. Existing adaptive clipping methods either modify the gradient update in vanilla DP-SGD, causing additional tuning or optimization overhead, or introduce separate private queries to monitor gradient statistics. In contrast, we leverage the *slack* information induced by the standard clipping operation, an overlooked signal in prior work, and show that it provides an effective indication for adapting $C$. In light of this, we propose *SlaClip*, a privacy-preserving adaptive clipping strategy using a post-hoc *Slack Indicator*. Under the same training configuration and privacy accountant, *SlaClip* preserves the sampling rule, noise multiplier, and global $\ell_2$ sensitivity bound of vanilla DP-SGD. Therefore, *SlaClip* is a plug-and-play module for vanilla DP-SGD and its variants. Moreover, *SlaClip* is accounted under the same per-step privacy bound, while requiring no additional private query. Across diverse datasets and tasks, experiments show that *SlaClip* consistently outperforms baseline adaptive clipping methods.