Inapproximability of VC Dimension and Littlestone's Dimension

Pasin Manurangsi; Aviad Rubinstein

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arXiv · 1705.09517

Inapproximability of VC Dimension and Littlestone's Dimension

Pasin Manurangsi·Aviad Rubinstein

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Abstract

We study the complexity of computing the VC Dimension and Littlestone's Dimension. Given an explicit description of a finite universe and a concept class (a binary matrix whose $(x,C)$-th entry is $1$ iff element $x$ belongs to concept $C$), both can be computed exactly in quasi-polynomial time ($n^{O(\log n)}$). Assuming the randomized Exponential Time Hypothesis (ETH), we prove nearly matching lower bounds on the running time, that hold even for approximation algorithms.

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Pasin Manurangsi, Aviad Rubinstein. 2017-05-26. Inapproximability of VC Dimension and Littlestone's Dimension. https://arxiv.org/abs/1705.09517

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