Find a witness or shatter: the landscape of computable PAC learning
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 hypothesis 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.
Keywords
Cite
@article{arxiv.2302.04731,
title = {Find a witness or shatter: the landscape of computable PAC learning},
author = {Valentino Delle Rose and Alexander Kozachinskiy and Cristobal Rojas and Tomasz Steifer},
journal= {arXiv preprint arXiv:2302.04731},
year = {2023}
}
Comments
12 pages, 1 figure (corrected version)