Semiparametric Efficient Bilevel Gradient Estimation
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911702287646720 |
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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 |