### Abstract

We investigate the query complexity of exact learning in the membership and (proper) equivalence query model. We give a complete characterization of concept classes that are learnable with a polynomial number of polynomial sized queries in this model. We give applications of this characterization, including results on learning a natural subclass of DNF formulas, and on learning with membership queries alone. Query complexity has previously been used to prove lower bounds on the time complexity of exact learning. We show a new relationship between query complexity and time complexity in exact learning: If any "honest" class is exactly and properly learnable with polynomial query complexity, but not learnable in polynomial time, then P ≠ NP. In particular, we show that an honest class is exactly polynomial-query learnable if and only if it is learnable using an oracle for Σ_{4}^{p}.

Original language | English (US) |
---|---|

Pages (from-to) | 840-862 |

Number of pages | 23 |

Journal | Journal of the ACM |

Volume | 43 |

Issue number | 5 |

State | Published - Sep 1996 |

### Fingerprint

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Graphics and Computer-Aided Design
- Hardware and Architecture
- Information Systems
- Software
- Theoretical Computer Science

### Cite this

*Journal of the ACM*,

*43*(5), 840-862.

**How many queries are needed to learn?** / Hellerstein, Lisa; Pillaipakkamnatt, Krishnan; Raghavan, Vijay; Wilkins, Dawn.

Research output: Contribution to journal › Article

*Journal of the ACM*, vol. 43, no. 5, pp. 840-862.

}

TY - JOUR

T1 - How many queries are needed to learn?

AU - Hellerstein, Lisa

AU - Pillaipakkamnatt, Krishnan

AU - Raghavan, Vijay

AU - Wilkins, Dawn

PY - 1996/9

Y1 - 1996/9

N2 - We investigate the query complexity of exact learning in the membership and (proper) equivalence query model. We give a complete characterization of concept classes that are learnable with a polynomial number of polynomial sized queries in this model. We give applications of this characterization, including results on learning a natural subclass of DNF formulas, and on learning with membership queries alone. Query complexity has previously been used to prove lower bounds on the time complexity of exact learning. We show a new relationship between query complexity and time complexity in exact learning: If any "honest" class is exactly and properly learnable with polynomial query complexity, but not learnable in polynomial time, then P ≠ NP. In particular, we show that an honest class is exactly polynomial-query learnable if and only if it is learnable using an oracle for Σ4p.

AB - We investigate the query complexity of exact learning in the membership and (proper) equivalence query model. We give a complete characterization of concept classes that are learnable with a polynomial number of polynomial sized queries in this model. We give applications of this characterization, including results on learning a natural subclass of DNF formulas, and on learning with membership queries alone. Query complexity has previously been used to prove lower bounds on the time complexity of exact learning. We show a new relationship between query complexity and time complexity in exact learning: If any "honest" class is exactly and properly learnable with polynomial query complexity, but not learnable in polynomial time, then P ≠ NP. In particular, we show that an honest class is exactly polynomial-query learnable if and only if it is learnable using an oracle for Σ4p.

UR - http://www.scopus.com/inward/record.url?scp=0030230237&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030230237&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030230237

VL - 43

SP - 840

EP - 862

JO - Journal of the ACM

JF - Journal of the ACM

SN - 0004-5411

IS - 5

ER -