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Effective Littlestone dimension
Proceedings of The 36th International Conference on Algorithmic Learning Theory, PMLR 272:405-417, 2025.
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.