On the non-efficient PAC learnability of conjunctive queries - ten Cate, Balder; Funk, Maurice; Jung, Jean Christoph; Lutz, Carsten (Information processing letters, 2024)
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. •Conjunctive Queries (CQs) are known to be not efficiently PAC learnable. We give a self-contained exposition.•Acyclic CQs are not efficiently PAC learnable, even for very restrictive notions of acyclicity.•Conjunctive Queries (CQs), and Unions of Conjunctive Queries (UCQs), are efficiently PAC learnable with membership queries.