  Privacy in AI remains a topic that draws attention from researchers and the
general public in recent years. As one way to implement privacy-preserving AI,
differentially private learning is a framework that enables AI models to use
differential privacy (DP). To achieve DP in the learning process, existing
algorithms typically limit the magnitude of gradients with a constant clipping,
which requires carefully tuned due to its significant impact on model
performance. As a solution to this issue, latest works NSGD and Auto-S
innovatively propose to use normalization instead of clipping to avoid
hyperparameter tuning. However, normalization-based approaches like NSGD and
Auto-S rely on a monotonic weight function, which imposes excessive weight on
small gradient samples and introduces extra deviation to the update. In this
paper, we propose a Differentially Private Per-Sample Adaptive Clipping
(DP-PSAC) algorithm based on a non-monotonic adaptive weight function, which
guarantees privacy without the typical hyperparameter tuning process of using a
constant clipping while significantly reducing the deviation between the update
and true batch-averaged gradient. We provide a rigorous theoretical convergence
analysis and show that with convergence rate at the same order, the proposed
algorithm achieves a lower non-vanishing bound, which is maintained over
training iterations, compared with NSGD/Auto-S. In addition, through extensive
experimental evaluation, we show that DP-PSAC outperforms or matches the
state-of-the-art methods on multiple main-stream vision and language tasks.
