  Differentially Private Stochastic Gradient Descent with Gradient Clipping
(DPSGD-GC) is a powerful tool for training deep learning models using sensitive
data, providing both a solid theoretical privacy guarantee and high efficiency.
However, using DPSGD-GC to ensure Differential Privacy (DP) comes at the cost
of model performance degradation due to DP noise injection and gradient
clipping. Existing research has extensively analyzed the theoretical
convergence of DPSGD-GC, and has shown that it only converges when using large
clipping thresholds that are dependent on problem-specific parameters.
Unfortunately, these parameters are often unknown in practice, making it hard
to choose the optimal clipping threshold. Therefore, in practice, DPSGD-GC
suffers from degraded performance due to the {\it constant} bias introduced by
the clipping.
  In our work, we propose a new error-feedback (EF) DP algorithm as an
alternative to DPSGD-GC, which not only offers a diminishing utility bound
without inducing a constant clipping bias, but more importantly, it allows for
an arbitrary choice of clipping threshold that is independent of the problem.
We establish an algorithm-specific DP analysis for our proposed algorithm,
providing privacy guarantees based on R{\'e}nyi DP. Additionally, we
demonstrate that under mild conditions, our algorithm can achieve nearly the
same utility bound as DPSGD without gradient clipping. Our empirical results on
Cifar-10/100 and E2E datasets, show that the proposed algorithm achieves higher
accuracies than DPSGD while maintaining the same level of DP guarantee.
