DP-AdamBC: Your DP-Adam Is Actually DP-SGD

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.