Effective Littlestone dimension

Published: 18 Dec 2024, Last Modified: 14 Feb 2025ALT 2025EveryoneRevisionsBibTeXCC BY 4.0
Abstract: Delle Rose et al.~(COLT'23) introduced an effective version of the Vapnik-Chervonenkis dimension, and showed that it characterizes improper PAC learning with total computable learners. In this paper, we introduce and study a similar effectivization of the notion of Littlestone dimension. Finite effective Littlestone dimension is a necessary condition for computable online learning but is not a sufficient one---which we already establish for classes of the effective Littlestone dimension 2. However, the effective Littlestone dimension equals the optimal mistake bound for computable learners in two special cases: a) for classes of Littlestone dimension 1 and b) when the learner receives as additional information an upper bound on the numbers to be guessed. Interestingly, a finite effective Littlestone dimension also guarantees that the class consists only of computable functions.
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Submission Number: 111
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