Adaptive Sampling for Private Worst-Case Group Optimization
Max Cairney-Leeming, Amartya Sanyal, Christoph H. Lampert
TL;DR
The paper addresses private max-min fairness in supervised learning by introducing ASC, a practical DP-DRO algorithm that adaptively samples per-group data and clips gradients to equalize privacy guarantees across groups. ASC achieves lower gradient variance and tighter privacy budgets, resulting in substantially better worst-case group accuracy without sacrificing average performance, outperforming standard DP-SGD and prior private DRO baselines. The approach combines per-group batch sizing, group-specific clipping thresholds, and Gaussian noise under Rényi-DP accounting, with formal guarantees and empirical validation on unbalanced datasets. The work provides a pathway to robust, privacy-preserving fair models in real-world, unevenly distributed data scenarios, and suggests extensions to multi-task and meta-learning settings.
Abstract
Models trained by minimizing the average loss often fail to be accurate on small or hard-to-learn groups of the data. Various methods address this issue by optimizing a weighted objective that focuses on the worst-performing groups. However, this approach becomes problematic when learning with differential privacy, as unequal data weighting can result in inhomogeneous privacy guarantees, in particular weaker privacy for minority groups. In this work, we introduce a new algorithm for differentially private worst-case group optimization called ASC (Adaptively Sampled and Clipped Worst-case Group Optimization). It adaptively controls both the sampling rate and the clipping threshold of each group. Thereby, it allows for harder-to-learn groups to be sampled more often while ensuring consistent privacy guarantees across all groups. Comparing ASC to prior work, we show that it results in lower-variance gradients, tighter privacy guarantees, and substantially higher worst-case group accuracy without sacrificing overall average accuracy.