Local Regularizers Are Not Transductive Learners

Sky Jafar, Julian Asilis, Shaddin Dughmi
Proceedings of Thirty Eighth Conference on Learning Theory, PMLR 291:2942-2957, 2025.

Abstract

We partly resolve an open question raised by Asilis et al. 2024: whether the algorithmic template of local regularization — an intriguing generalization of explicit regularization, a.k.a. structural risk minimization — suffices to learn all learnable multiclass problems. Specifically, we provide a negative answer to this question in the transductive model of learning. We exhibit a multiclass classification problem which is learnable in both the transductive and PAC models, yet cannot be learned transductively by any local regularizer. The corresponding hypothesis class, and our proof, are based on principles from cryptographic secret sharing. We outline challenges in extending our negative result to the PAC model, leaving open the tantalizing possibility of a PAC/transductive separation with respect to local regularization.

Cite this Paper

BibTeX
@InProceedings{pmlr-v291-jafar25a, title = {Local Regularizers Are Not Transductive Learners}, author = {Jafar, Sky and Asilis, Julian and Dughmi, Shaddin}, booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory}, pages = {2942--2957}, 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/jafar25a/jafar25a.pdf}, url = {https://proceedings.mlr.press/v291/jafar25a.html}, abstract = {We partly resolve an open question raised by Asilis et al. 2024: whether the algorithmic template of local regularization — an intriguing generalization of explicit regularization, a.k.a. structural risk minimization — suffices to learn all learnable multiclass problems. Specifically, we provide a negative answer to this question in the transductive model of learning. We exhibit a multiclass classification problem which is learnable in both the transductive and PAC models, yet cannot be learned transductively by any local regularizer. The corresponding hypothesis class, and our proof, are based on principles from cryptographic secret sharing. We outline challenges in extending our negative result to the PAC model, leaving open the tantalizing possibility of a PAC/transductive separation with respect to local regularization.} }
Endnote
%0 Conference Paper %T Local Regularizers Are Not Transductive Learners %A Sky Jafar %A Julian Asilis %A Shaddin Dughmi %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-jafar25a %I PMLR %P 2942--2957 %U https://proceedings.mlr.press/v291/jafar25a.html %V 291 %X We partly resolve an open question raised by Asilis et al. 2024: whether the algorithmic template of local regularization — an intriguing generalization of explicit regularization, a.k.a. structural risk minimization — suffices to learn all learnable multiclass problems. Specifically, we provide a negative answer to this question in the transductive model of learning. We exhibit a multiclass classification problem which is learnable in both the transductive and PAC models, yet cannot be learned transductively by any local regularizer. The corresponding hypothesis class, and our proof, are based on principles from cryptographic secret sharing. We outline challenges in extending our negative result to the PAC model, leaving open the tantalizing possibility of a PAC/transductive separation with respect to local regularization.
APA
Jafar, S., Asilis, J. & Dughmi, S.. (2025). Local Regularizers Are Not Transductive Learners. Proceedings of Thirty Eighth Conference on Learning Theory, in Proceedings of Machine Learning Research 291:2942-2957 Available from https://proceedings.mlr.press/v291/jafar25a.html.

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