DP-Adam: Correcting DP Bias in Adam's Second Moment Estimation

04/21/2023

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by   Qiaoyue Tang, et al.

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We observe that the traditional use of DP with the Adam optimizer introduces a bias in the second moment estimation, due to the addition of independent noise in the gradient computation. This bias leads to a different scaling for low variance parameter updates, that is inconsistent with the behavior of non-private Adam, and Adam's sign descent interpretation. Empirically, correcting the bias introduced by DP noise significantly improves the optimization performance of DP-Adam.