A theoretical and empirical study finds that unbiased second-moment estimates in private Adam can be harmful in high dimensions, and that scale-then-privatize outperforms the alternatives on a small transformer task.
Continual Release Moment Estimation with Differential Privacy
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abstract
We propose Joint Moment Estimation (JME), a method for continually and privately estimating both the first and second moments of data with reduced noise compared to naive approaches. JME uses the matrix mechanism and a joint sensitivity analysis to allow the second moment estimation with no additional privacy cost, thereby improving accuracy while maintaining privacy. We demonstrate JME's effectiveness in two applications: estimating the running mean and covariance matrix for Gaussian density estimation, and model training with DP-Adam on CIFAR-10.
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On Design Principles for Private Adaptive Optimizers
A theoretical and empirical study finds that unbiased second-moment estimates in private Adam can be harmful in high dimensions, and that scale-then-privatize outperforms the alternatives on a small transformer task.