Find a witness or shatter: the landscape of computable PAC learning.

Valentino Delle Rose, Alexander Kozachinskiy, Cristóbal Rojas, Tomasz Steifer
Proceedings of Thirty Sixth Conference on Learning Theory, PMLR 195:511-524, 2023.

Abstract

This paper contributes to the study of CPAC learnability —a computable version of PAC learning– by solving three open questions from recent papers. Firstly, we prove that every improperly CPAC learnable class is contained in a class which is properly CPAC learnable with polynomial sample complexity. This confirms a conjecture by Agarwal et al (COLT 2021). Secondly, we show that there exists a decidable class of hypotheses which is properly CPAC learnable, but only with uncomputably fast-growing sample complexity. This solves a question from Sterkenburg (COLT 2022). Finally, we construct a decidable class of finite Littlestone dimension which is not improperly CPAC learnable, strengthening a recent result of Sterkenburg (2022) and answering a question posed by Hasrati and Ben-David (ALT 2023). Together with previous work, our results provide a complete landscape for the learnability problem in the CPAC setting.

Cite this Paper

BibTeX
@InProceedings{pmlr-v195-delle-rose23a, title = {Find a witness or shatter: the landscape of computable PAC learning.}, author = {Delle Rose, Valentino and Kozachinskiy, Alexander and Rojas, Crist{\'o}bal and Steifer, Tomasz}, booktitle = {Proceedings of Thirty Sixth Conference on Learning Theory}, pages = {511--524}, year = {2023}, editor = {Neu, Gergely and Rosasco, Lorenzo}, volume = {195}, series = {Proceedings of Machine Learning Research}, month = {12--15 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v195/delle-rose23a/delle-rose23a.pdf}, url = {https://proceedings.mlr.press/v195/delle-rose23a.html}, abstract = { This paper contributes to the study of CPAC learnability —a computable version of PAC learning– by solving three open questions from recent papers. Firstly, we prove that every improperly CPAC learnable class is contained in a class which is properly CPAC learnable with polynomial sample complexity. This confirms a conjecture by Agarwal et al (COLT 2021). Secondly, we show that there exists a decidable class of hypotheses which is properly CPAC learnable, but only with uncomputably fast-growing sample complexity. This solves a question from Sterkenburg (COLT 2022). Finally, we construct a decidable class of finite Littlestone dimension which is not improperly CPAC learnable, strengthening a recent result of Sterkenburg (2022) and answering a question posed by Hasrati and Ben-David (ALT 2023). Together with previous work, our results provide a complete landscape for the learnability problem in the CPAC setting. } }
Endnote
%0 Conference Paper %T Find a witness or shatter: the landscape of computable PAC learning. %A Valentino Delle Rose %A Alexander Kozachinskiy %A Cristóbal Rojas %A Tomasz Steifer %B Proceedings of Thirty Sixth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2023 %E Gergely Neu %E Lorenzo Rosasco %F pmlr-v195-delle-rose23a %I PMLR %P 511--524 %U https://proceedings.mlr.press/v195/delle-rose23a.html %V 195 %X This paper contributes to the study of CPAC learnability —a computable version of PAC learning– by solving three open questions from recent papers. Firstly, we prove that every improperly CPAC learnable class is contained in a class which is properly CPAC learnable with polynomial sample complexity. This confirms a conjecture by Agarwal et al (COLT 2021). Secondly, we show that there exists a decidable class of hypotheses which is properly CPAC learnable, but only with uncomputably fast-growing sample complexity. This solves a question from Sterkenburg (COLT 2022). Finally, we construct a decidable class of finite Littlestone dimension which is not improperly CPAC learnable, strengthening a recent result of Sterkenburg (2022) and answering a question posed by Hasrati and Ben-David (ALT 2023). Together with previous work, our results provide a complete landscape for the learnability problem in the CPAC setting.
APA
Delle Rose, V., Kozachinskiy, A., Rojas, C. & Steifer, T.. (2023). Find a witness or shatter: the landscape of computable PAC learning.. Proceedings of Thirty Sixth Conference on Learning Theory, in Proceedings of Machine Learning Research 195:511-524 Available from https://proceedings.mlr.press/v195/delle-rose23a.html.

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