A Map of Update Constraints in Inductive Inference

TL;DR

This paper maps out how various learning restrictions affect inductive inference capabilities, providing a comprehensive overview of their relationships and properties for delayable restrictions.

Contribution

It offers a complete map of nine learning restrictions for complete and set-driven learning, completing the understanding of delayable restrictions in inductive inference.

Findings

Complete characterization of nine restrictions for delayable learning.

Learners with delayable restrictions can be assumed total.

New characterizations of conservative versus cautious learning.

Abstract

We investigate how different learning restrictions reduce learning power and how the different restrictions relate to one another. We give a complete map for nine different restrictions both for the cases of complete information learning and set-driven learning. This completes the picture for these well-studied \emph{delayable} learning restrictions. A further insight is gained by different characterizations of \emph{conservative} learning in terms of variants of \emph{cautious} learning. Our analyses greatly benefit from general theorems we give, for example showing that learners with exclusively delayable restrictions can always be assumed total.