On characterizations of learnability with computable learners
Abstract
We study computable PAC (CPAC) learning as introduced by Agarwal et al. (2020). First, we consider the main open question of finding characterizations of proper and improper CPAC learning. We give a characterization of a closely related notion of strong CPAC learning, and provide a negative answer to the COLT open problem posed by Agarwal et al. (2021) whether all decidably representable VC classes are improperly CPAC learnable. Second, we consider undecidability of (computable) PAC learnability. We give a simple general argument to exhibit such ndecidability, and initiate a study of the arithmetical complexity of learnability. We briefly discuss the relation to the undecidability result of Ben-David et al. (2019), that motivated the work of Agarwal et al.
Keywords
Cite
@article{arxiv.2202.05041,
title = {On characterizations of learnability with computable learners},
author = {Tom F. Sterkenburg},
journal= {arXiv preprint arXiv:2202.05041},
year = {2022}
}
Comments
Final version, as accepted for COLT 2022. Changes w.r.t. previous arXiv version: In response to reviewer comments, major revision of the discussion in Section 3.2, incl. reformulation of Question 2 (that in its original form had an easy answer) and retraction of Definition 6 and Proposition 2 (that lost their relevance in the revised discussion). Minor textual revisions elsewhere