提出一种无偏双层梯度估计方法，解决非参数学习带来的偏差问题。
Semiparametric Efficient Bilevel Gradient Estimation
- 基于高效影响函数构建半参数去偏理论
- 在二次损失下实现双重稳健的得分估计
- 在合成数据上优于传统插值和正则化核方法
函数型双层方法通过估计低层函数并代入超梯度，但在非参数学习低层问题时，这种代入梯度可能保留一阶偏差。为消除该偏差，我们基于高效影响函数发展了针对总体双层梯度的半参数去偏理论。该视角导出一种交叉拟合的正交超梯度估计器，我们建立了其渐近正态性，并实现了对外层参数的统一控制。在二次损失下，该估计器简化为基于条件均值干扰项的双重稳健得分。在具有已知真值的合成双层基准测试中，该方法追踪到了最优高效梯度基准，且优于插值函数超梯度和正则化核双层基线方法。
原文摘要 · Abstract (English)
Functional bilevel methods estimate a lower-level function and plug it into a hypergradient, but this plug-in gradient can retain first-order bias when the lower-level problem is learned nonparametrically. To remove this bias, we develop a semiparametric debiasing theory for population bilevel gradients based on the efficient influence function. This perspective leads to a cross-fitted orthogonal hypergradient estimator for which we establish asymptotic normality together with uniform control over the outer parameter. Under quadratic losses, the estimator reduces to a simple doubly robust score based on conditional mean nuisances. On synthetic bilevel benchmarks with known ground truth, the method tracks the oracle efficient-gradient benchmark and improves over plug-in functional hypergradients and regularized kernel bilevel baselines.
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