Semiparametric Efficient Bilevel Gradient Estimation

TL;DR

This paper introduces a semiparametric debiasing approach for bilevel gradient estimation, reducing bias and improving accuracy in hyperparameter optimization tasks.

Contribution

It develops a novel semiparametric theory and a cross-fitted orthogonal hypergradient estimator that achieves asymptotic normality and reduces bias in bilevel problems.

Findings

Estimator tracks oracle efficient-gradient benchmark on synthetic data.

Method outperforms plug-in hypergradients and kernel baselines.

Under quadratic loss, reduces to a doubly robust score.

Abstract

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.