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

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 query mechanisms 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, both *SlaClip*-DP-SGD and vanilla DP-SGD instantiate the identical Gaussian mechanism, and therefore incur equivalent privacy cost. Moreover, it requires minimal task-specific hyperparameter tuning and exhibits robust performance improvement across diverse datasets and model architectures.