Tight Bounds on Proper Equivalence Query Learning of DNF

TL;DR

This paper introduces a new structural lemma for partial Boolean functions, leading to the first subexponential proper learning algorithm for DNF in the EQ model, with optimal complexity.

Contribution

It presents a novel seed lemma for DNF and develops the first subexponential proper learning algorithm in the EQ model, along with related results on DNF certificates and PAC-learning.

Findings

First subexponential proper DNF learning algorithm in EQ model

Optimal time and query complexity of 2^{(O(√n))}

New results on DNF-size certificates and PAC-learning DNF

Abstract

We prove a new structural lemma for partial Boolean functions $f$, which we call the seed lemma for DNF. Using the lemma, we give the first subexponential algorithm for proper learning of DNF in Angluin's Equivalence Query (EQ) model. The algorithm has time and query complexity $2^{(\tilde{O}{\sqrt{n}})}$, which is optimal. We also give a new result on certificates for DNF-size, a simple algorithm for properly PAC-learning DNF, and new results on EQ-learning $\log n$-term DNF and decision trees.