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arXiv · 2206.13257

Finite Littlestone Dimension Implies Finite Information Complexity

Aditya Pradeep·Ido Nachum·Michael Gastpar
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Abstract

We prove that every online learnable class of functions of Littlestone dimension $d$ admits a learning algorithm with finite information complexity. Towards this end, we use the notion of a globally stable algorithm. Generally, the information complexity of such a globally stable algorithm is large yet finite, roughly exponential in $d$. We also show there is room for improvement; for a canonical online learnable class, indicator functions of affine subspaces of dimension $d$, the information complexity can be upper bounded logarithmically in $d$.

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Aditya Pradeep, Ido Nachum, Michael Gastpar. 2022-06-27. Finite Littlestone Dimension Implies Finite Information Complexity. https://arxiv.org/abs/2206.13257

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