Applications of Littlestone dimension to query learning and to compression

TL;DR

This paper explores the applications of Littlestone dimension in query learning and compression, extending existing models to infinite classes and improving theoretical bounds related to compression schemes.

Contribution

It extends previous results on Littlestone dimension to infinite concept classes with randomness and proves a strong version of a conjecture relating Littlestone dimension to compression schemes.

Findings

Extended learning models to infinite classes with randomness

Improved bounds on Littlestone dimension and compression schemes

Proved a strong version of a conjecture on Littlestone dimension

Abstract

In this paper we give several applications of Littlestone dimension. The first is to the model of \cite{angluin2017power}, where we extend their results for learning by equivalence queries with random counterexamples. Second, we extend that model to infinite concept classes with an additional source of randomness. Third, we give improved results on the relationship of Littlestone dimension to classes with extended $d$-compression schemes, proving a strong version of a conjecture of \cite{floyd1995sample} for Littlestone dimension.