On the non-efficient PAC learnability of conjunctive queries

TL;DR

This paper demonstrates that conjunctive queries are not efficiently PAC learnable in the standard model, but they are learnable with membership queries, and extends these results to various restricted classes.

Contribution

It provides a detailed proof that conjunctive queries lack efficient PAC learnability without membership queries and extends this negative result to many subclasses, while also showing learnability with membership queries.

Findings

Conjunctive queries are not efficiently PAC learnable in the standard model.

Many restricted classes of conjunctive queries are also not efficiently PAC learnable.

Conjunctive and UCQs are efficiently PAC learnable with membership queries.

Abstract

This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating fact that this concept class lacks the polynomial-size fitting property, a property that is tacitly assumed in much of the computational learning theory literature; (ii) we establish a strong negative PAC learnability result that applies to many restricted classes of conjunctive queries (CQs), including acyclic CQs for a wide range of notions of "acyclicity"; (iii) we show that CQs (and UCQs) are efficiently PAC learnable with membership queries.