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Behaviorally Correct Learning from Informants

Niklas Mohrin

TL;DR

This work investigates the learnability of recursively enumerable languages when learning from informants under behaviorally correct identification. It develops a rigorous framework distinguishing delayable and semantic learning restrictions, and maps how monotonic and dual monotonic variants relate, including cautiousness and consistency constraints. The results show that BC-learning from informants can exceed explanatory learning in power, and that many monotonicity constraints can be preserved under patching to achieve global consistency, with poisoning providing a tool for dual weak monotonicity. The study yields a detailed map of restriction interactions, establishes key separations between classic and dual variants, and outlines several avenues for future semantic learning research and normal-form results.

Abstract

In inductive inference, we investigate the learnability of classes of formal languages. We are interested in what classes of languages are learnable in certain learning settings. A class of languages is learnable, if there is a learner that can identify all of its languages and satisfies the constraints of the learning setting. To identify a language, a learner is presented with information about this very language. When learning from informants, this information consists of examples for numbers that are, and numbers that are not included in the target language. As more and more examples are presented, the learner outputs a hypothesis sequence. To satisfy behaviorally correct identification, this hypothesis sequence must eventually only list correct labels for the target language. In this thesis, we compare the effects of a number of semantic learning restrictions on the learning capabilities for behaviorally correct learning from informants.

Behaviorally Correct Learning from Informants

TL;DR

This work investigates the learnability of recursively enumerable languages when learning from informants under behaviorally correct identification. It develops a rigorous framework distinguishing delayable and semantic learning restrictions, and maps how monotonic and dual monotonic variants relate, including cautiousness and consistency constraints. The results show that BC-learning from informants can exceed explanatory learning in power, and that many monotonicity constraints can be preserved under patching to achieve global consistency, with poisoning providing a tool for dual weak monotonicity. The study yields a detailed map of restriction interactions, establishes key separations between classic and dual variants, and outlines several avenues for future semantic learning research and normal-form results.

Abstract

In inductive inference, we investigate the learnability of classes of formal languages. We are interested in what classes of languages are learnable in certain learning settings. A class of languages is learnable, if there is a learner that can identify all of its languages and satisfies the constraints of the learning setting. To identify a language, a learner is presented with information about this very language. When learning from informants, this information consists of examples for numbers that are, and numbers that are not included in the target language. As more and more examples are presented, the learner outputs a hypothesis sequence. To satisfy behaviorally correct identification, this hypothesis sequence must eventually only list correct labels for the target language. In this thesis, we compare the effects of a number of semantic learning restrictions on the learning capabilities for behaviorally correct learning from informants.

Paper Structure

This paper contains 31 sections, 32 theorems, 42 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related work
  4. Preliminaries
  5. Informants
  6. Interaction operators
  7. Learning restrictions
  8. Properties of learning restrictions
  9. General observations
  10. Delayable restrictions
  11. Semantic restrictions
  12. Separation from explanatory learning
  13. Case 1: $L$ is infinite.
  14. Case 2: $L$ is finite.
  15. Cautiousness
  16. ...and 16 more sections

Key Result

Theorem 1

For any delayable $\delta$, we have $[\mathbf{Inf}_{\textup{can}}\mathbf{G}\delta] = [\mathbf{Inf}\mathbf{Sd}\delta]$.

Figures (1)

  • Figure 1: Relations between monotonicity constraints in $\mathbf{Inf}\mathbf{Bc}$-learning. Black lines indicate inclusions. Two learning restrictions are equivalent if and only if they lie in the same gray box. For all displayed restrictions, learners can additionally be assumed to be set-driven, total and globally consistent.

Theorems & Definitions (63)

  • Theorem 1: aschenbach2018learning
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • Theorem 4
  • proof
  • Corollary 1
  • Theorem 5: aschenbach2018learning
  • proof
  • ...and 53 more