  The Adam optimizer is a popular choice in contemporary deep learning, due to
its strong empirical performance. However we observe that in privacy sensitive
scenarios, the traditional use of Differential Privacy (DP) with the Adam
optimizer leads to sub-optimal performance on several tasks. We find that this
performance degradation is due to a DP bias in Adam's second moment estimator,
introduced by the addition of independent noise in the gradient computation to
enforce DP guarantees. This DP bias leads to a different scaling for low
variance parameter updates, that is inconsistent with the behavior of
non-private Adam. We propose DP-AdamBC, an optimization algorithm which removes
the bias in the second moment estimation and retrieves the expected behaviour
of Adam. Empirically, DP-AdamBC significantly improves the optimization
performance of DP-Adam by up to 3.5% in final accuracy in image, text, and
graph node classification tasks.
