Open Problem: Structure-Agnostic Minimax Risk for Partial Linear Model

Yihong Gu
Proceedings of Thirty Eighth Conference on Learning Theory, PMLR 291:6220-6224, 2025.

Abstract

Double machine learning is a theoretically grounded and practically efficient procedure for a variety of causal estimands and functional estimation problems when adopting black-box machine learning models for estimating nuisance parameters. It is known that double machine learning may have sub-optimal performance in the structure-aware settings, e.g., the nuisances are H{ö}lder smooth functions, and recent articles (Balakrishnan et al., 2023) are delivering the message that double machine learning is optimal in structure-agnostic settings. This note claims that whether double machine learning is optimal for black-box machine learning models remains open, even for the simplest linear coefficient estimation in the partial linear model. We argue that the key gap that differentiates structure-agnostic and structure-aware settings, and also the previous lower bound results do not address, is the role of variance – the awareness of well-conditioned structures offers the possibility to mitigate the effects of variance, while that is not clear for structure-agnostic settings. The answer to this question has significant implications both in theory and practice.

Cite this Paper

BibTeX
@InProceedings{pmlr-v291-gu25b, title = {Open Problem: Structure-Agnostic Minimax Risk for Partial Linear Model}, author = {Gu, Yihong}, booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory}, pages = {6220--6224}, year = {2025}, editor = {Haghtalab, Nika and Moitra, Ankur}, volume = {291}, series = {Proceedings of Machine Learning Research}, month = {30 Jun--04 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v291/main/assets/gu25b/gu25b.pdf}, url = {https://proceedings.mlr.press/v291/gu25b.html}, abstract = {Double machine learning is a theoretically grounded and practically efficient procedure for a variety of causal estimands and functional estimation problems when adopting black-box machine learning models for estimating nuisance parameters. It is known that double machine learning may have sub-optimal performance in the structure-aware settings, e.g., the nuisances are H{ö}lder smooth functions, and recent articles (Balakrishnan et al., 2023) are delivering the message that double machine learning is optimal in structure-agnostic settings. This note claims that whether double machine learning is optimal for black-box machine learning models remains open, even for the simplest linear coefficient estimation in the partial linear model. We argue that the key gap that differentiates structure-agnostic and structure-aware settings, and also the previous lower bound results do not address, is the role of variance – the awareness of well-conditioned structures offers the possibility to mitigate the effects of variance, while that is not clear for structure-agnostic settings. The answer to this question has significant implications both in theory and practice. } }
Endnote
%0 Conference Paper %T Open Problem: Structure-Agnostic Minimax Risk for Partial Linear Model %A Yihong Gu %B Proceedings of Thirty Eighth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2025 %E Nika Haghtalab %E Ankur Moitra %F pmlr-v291-gu25b %I PMLR %P 6220--6224 %U https://proceedings.mlr.press/v291/gu25b.html %V 291 %X Double machine learning is a theoretically grounded and practically efficient procedure for a variety of causal estimands and functional estimation problems when adopting black-box machine learning models for estimating nuisance parameters. It is known that double machine learning may have sub-optimal performance in the structure-aware settings, e.g., the nuisances are H{ö}lder smooth functions, and recent articles (Balakrishnan et al., 2023) are delivering the message that double machine learning is optimal in structure-agnostic settings. This note claims that whether double machine learning is optimal for black-box machine learning models remains open, even for the simplest linear coefficient estimation in the partial linear model. We argue that the key gap that differentiates structure-agnostic and structure-aware settings, and also the previous lower bound results do not address, is the role of variance – the awareness of well-conditioned structures offers the possibility to mitigate the effects of variance, while that is not clear for structure-agnostic settings. The answer to this question has significant implications both in theory and practice.
APA
Gu, Y.. (2025). Open Problem: Structure-Agnostic Minimax Risk for Partial Linear Model. Proceedings of Thirty Eighth Conference on Learning Theory, in Proceedings of Machine Learning Research 291:6220-6224 Available from https://proceedings.mlr.press/v291/gu25b.html.

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