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PAC Learning, VC Dimension, and the Arithmetic Hierarchy
Published 4 Jun 2014 in math.LO, cs.LG, and cs.LO | (1406.1111v1)
Abstract: We compute that the index set of PAC-learnable concept classes is $m$-complete $\Sigma0_3$ within the set of indices for all concept classes of a reasonable form. All concept classes considered are computable enumerations of computable $\Pi0_1$ classes, in a sense made precise here. This family of concept classes is sufficient to cover all standard examples, and also has the property that PAC learnability is equivalent to finite VC dimension.
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