Collaborative Learning with Different Labeling Functions

Yuyang Deng, Mingda Qiao
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:10530-10552, 2024.

Abstract

We study a variant of Collaborative PAC Learning, in which we aim to learn an accurate classifier for each of the $n$ data distributions, while minimizing the number of samples drawn from them in total. Unlike in the usual collaborative learning setup, it is not assumed that there exists a single classifier that is simultaneously accurate for all distributions. We show that, when the data distributions satisfy a weaker realizability assumption, which appeared in (Crammer & Mansour, 2012) in the context of multi-task learning, sample-efficient learning is still feasible. We give a learning algorithm based on Empirical Risk Minimization (ERM) on a natural augmentation of the hypothesis class, and the analysis relies on an upper bound on the VC dimension of this augmented class. In terms of the computational efficiency, we show that ERM on the augmented hypothesis class is $\mathsf{NP}$-hard, which gives evidence against the existence of computationally efficient learners in general. On the positive side, for two special cases, we give learners that are both sample- and computationally-efficient.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-deng24d, title = {Collaborative Learning with Different Labeling Functions}, author = {Deng, Yuyang and Qiao, Mingda}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {10530--10552}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/deng24d/deng24d.pdf}, url = {https://proceedings.mlr.press/v235/deng24d.html}, abstract = {We study a variant of Collaborative PAC Learning, in which we aim to learn an accurate classifier for each of the $n$ data distributions, while minimizing the number of samples drawn from them in total. Unlike in the usual collaborative learning setup, it is not assumed that there exists a single classifier that is simultaneously accurate for all distributions. We show that, when the data distributions satisfy a weaker realizability assumption, which appeared in (Crammer & Mansour, 2012) in the context of multi-task learning, sample-efficient learning is still feasible. We give a learning algorithm based on Empirical Risk Minimization (ERM) on a natural augmentation of the hypothesis class, and the analysis relies on an upper bound on the VC dimension of this augmented class. In terms of the computational efficiency, we show that ERM on the augmented hypothesis class is $\mathsf{NP}$-hard, which gives evidence against the existence of computationally efficient learners in general. On the positive side, for two special cases, we give learners that are both sample- and computationally-efficient.} }
Endnote
%0 Conference Paper %T Collaborative Learning with Different Labeling Functions %A Yuyang Deng %A Mingda Qiao %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-deng24d %I PMLR %P 10530--10552 %U https://proceedings.mlr.press/v235/deng24d.html %V 235 %X We study a variant of Collaborative PAC Learning, in which we aim to learn an accurate classifier for each of the $n$ data distributions, while minimizing the number of samples drawn from them in total. Unlike in the usual collaborative learning setup, it is not assumed that there exists a single classifier that is simultaneously accurate for all distributions. We show that, when the data distributions satisfy a weaker realizability assumption, which appeared in (Crammer & Mansour, 2012) in the context of multi-task learning, sample-efficient learning is still feasible. We give a learning algorithm based on Empirical Risk Minimization (ERM) on a natural augmentation of the hypothesis class, and the analysis relies on an upper bound on the VC dimension of this augmented class. In terms of the computational efficiency, we show that ERM on the augmented hypothesis class is $\mathsf{NP}$-hard, which gives evidence against the existence of computationally efficient learners in general. On the positive side, for two special cases, we give learners that are both sample- and computationally-efficient.
APA
Deng, Y. & Qiao, M.. (2024). Collaborative Learning with Different Labeling Functions. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:10530-10552 Available from https://proceedings.mlr.press/v235/deng24d.html.

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