arXiv 2302.047312023-02-23cs.CCcs.LGmath.LOstat.ML

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

Centro Nacional de Inteligencia Artificial（国家人工智能中心）；Instituto de Ingeniería Matemática y Computacional, Universidad Católica de Chile（智利天主教大学数学与计算工程学院）；Instituto Milenio Fundamentos de los Datos（数据基础千年研究所）；Institute of Fundamental Technological Research, Polish Academy of Sciences（波兰科学院基础技术研究所）

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

备注：: 12 pages, 1 figure (corrected version)

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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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