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

Valentino Delle Rose; Alexander Kozachinskiy; Cristobal Rojas; Tomasz Steifer

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arXiv · 2302.04731

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

Valentino Delle Rose·Alexander Kozachinskiy·Cristobal Rojas·Tomasz Steifer

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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.

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Valentino Delle Rose, Alexander Kozachinskiy, Cristobal Rojas, Tomasz Steifer. 2023-02-06. Find a witness or shatter: the landscape of computable PAC learning. https://arxiv.org/abs/2302.04731

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