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

Qiaoyue Tang; Alain Zhiyanov; Mathias Lécuyer

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arXiv · 2507.10536

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

Qiaoyue Tang·Alain Zhiyanov·Mathias Lécuyer

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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.

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Qiaoyue Tang, Alain Zhiyanov, Mathias Lécuyer. 2025-07-14. On the Performance of Differentially Private Optimization with Heavy-Tail Class Imbalance. https://arxiv.org/abs/2507.10536

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