提出新公平性度量，直接优化预测公平与准确的权衡。
Functional Bilevel Optimization for Predictive Fairness
- 用条件均值方差衡量公平性，构建函数型双层优化问题。
- 两种算法在合成与真实数据上均实现最低公平-准确损失。
- 适用于高维连续敏感属性场景，优于现有对抗与核方法。
当敏感属性为连续高维（如人口评分向量、年龄或收入分布）时，强制完全统计独立性过于严格；现有松弛方法依赖间接依赖惩罚或对抗机制，未直接针对公平性-准确性权衡。本文提出通过DPVar（敏感属性条件下预测均值的方差）实现均值层面的群体公平性，并证明其对应函数型双层优化问题。为此设计两种算法：FBO利用平方损失下的闭式伴随法获得精确超梯度；ITD则通过展开内层步骤进行反向传播，可扩展至非平方损失。在合成数据和基于60个表格回归数据集构建的新半合成基准上，两者均实现最低或接近最低的总体公平-准确遗憾，且一致优于强基线方法（包括HSIC、对抗、线性依赖及广义均值公平性方法）。
原文摘要 · Abstract (English)
When sensitive attributes are continuous and high-dimensional $-$ demographic score vectors, posteriors over attributes, age or income profiles $-$ enforcing full statistical independence is often too restrictive, and existing relaxations rely on indirect dependence penalties or adversarial schemes that do not directly target the fairness-accuracy trade-off. We instead consider mean demographic parity through DPVar, the variance of the conditional-mean prediction given the sensitive attribute, and show that optimizing it yields a functional bilevel problem. We propose two algorithms for this problem: FBO, which uses a closed-form adjoint we derive for the squared-loss case to obtain an exact hypergradient, and ITD, which differentiates through unrolled inner steps and extends beyond squared loss. On synthetic data and a new semi-synthetic benchmark built from 60 tabular regression datasets, both methods achieve the lowest or near-lowest aggregate fairness-accuracy regret, and consistently match or outperform strong HSIC, adversarial, linear-dependence, and generalized-DP baselines.
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