Learning from Informants: Relations between Learning Success Criteria

TL;DR

This paper explores the theoretical relationships between different success criteria in learning from informants, emphasizing delayability, conservative learning, and hierarchies involving anomalies and vacillations.

Contribution

It establishes the main theorem linking delayable success criteria, analyzes the structural property of delayability, and introduces a hierarchy based on anomalies and vacillations in informant learning.

Findings

Delayability is a key structural property for understanding learning success criteria.

A hierarchy of learning success criteria based on the number of anomalies is established.

Duality in vacillations depending on their finiteness is observed in the learning process.

Abstract

Learning from positive and negative information, so-called \emph{informants}, being one of the models for human and machine learning introduced by E.~M.~Gold, is investigated. Particularly, naturally arising questions about this learning setting, originating in results on learning from solely positive information, are answered. By a carefully arranged argument learners can be assumed to only change their hypothesis in case it is inconsistent with the data (such a learning behavior is called \emph{conservative}). The deduced main theorem states the relations between the most important delayable learning success criteria, being the ones not ruined by a delayed in time hypothesis output. Additionally, our investigations concerning the non-delayable requirement of consistent learning underpin the claim for \emph{delayability} being the right structural property to gain a deeper understanding concerning the nature of learning success criteria. Moreover, we obtain an anomalous \emph{hierarchy} when allowing for an increasing finite number of \emph{anomalies} of the hypothesized language by the learner compared with the language to be learned. In contrast to the vacillatory hierarchy for learning from solely positive information, we observe a \emph{duality} depending on whether infinitely many \emph{vacillations} between different (almost) correct hypotheses are still considered a successful learning behavior.