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

Differentially private stochastic gradient descent (DP-SGD) achieves privacy by clipping persample 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 ℓ 2 sensitivity bound of vanilla DP-SGD. Therefore, SlaClip is a plug-andplay 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.