On the Performance of Differentially Private Optimization with Heavy-Tail Class Imbalance

TL;DR

This paper investigates how different private optimization algorithms perform under heavy-tail class imbalance, highlighting the advantages of second-order methods like DP-AdamBC in improving accuracy for rare classes.

Contribution

It demonstrates that second-order estimation methods mitigate the negative effects of heavy-tail class imbalance in differentially private learning, improving accuracy on infrequent classes.

Findings

DP-AdamBC reduces bias in loss curvature estimation.

Training accuracy for rare classes improves by approximately 8% and 5%.

Second-order methods outperform first-order in imbalanced private learning.

Abstract

In this work, we analyze the optimization behaviour of common private learning optimization algorithms under heavy-tail class imbalanced distribution. We show that, in a stylized model, optimizing with Gradient Descent with differential privacy (DP-GD) suffers when learning low-frequency classes, whereas optimization algorithms that estimate second-order information do not. In particular, DP-AdamBC that removes the DP bias from estimating loss curvature is a crucial component to avoid the ill-condition caused by heavy-tail class imbalance, and empirically fits the data better with $\approx8\%$ and $\approx5\%$ increase in training accuracy when learning the least frequent classes on both controlled experiments and real data respectively.