Semiparametric Efficient Bilevel Gradient Estimation

Fuente: arXiv
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Autori principali: Khoury, Fares El, Zenati, Houssam, Kallus, Nathan, Arbel, Michael, Bibaut, Aurélien
Natura: Preprint
Pubblicazione: 2026
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author Khoury, Fares El
Zenati, Houssam
Kallus, Nathan
Arbel, Michael
Bibaut, Aurélien
author_facet Khoury, Fares El
Zenati, Houssam
Kallus, Nathan
Arbel, Michael
Bibaut, Aurélien
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_21341
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Semiparametric Efficient Bilevel Gradient Estimation
Khoury, Fares El
Zenati, Houssam
Kallus, Nathan
Arbel, Michael
Bibaut, Aurélien
Machine Learning
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.
title Semiparametric Efficient Bilevel Gradient Estimation
topic Machine Learning
url https://arxiv.org/abs/2605.21341