DNF—if you can't learn'em, teach'em: an interactive model of teaching

Previous teaching models in the learning theory community have all been batch models. That is, in these models the teacher has generated a single set of helpful examples to present to the learner. In this paper we present an interactive model in which the learner has the ability to ask queries as in the query learning model of Angluin [1]. We show that this model is at least as powerful as previous teaching models. We also show that anything learnable with queries, even by a randomized learner, is teachable in our model. In all previous teaching models, all classes shown to be teachable are known to be efficiently learnable. An important concept class that is not known to be learnable is DNF formulas. We demonstrate the power of our approach by providing a deterministic teacher and learner for the class of DNF formulas, The learner makes only equivalence queries and all hypotheses are also DNF formulas. We consider several implications of our model when combined with other results and prove several general theorems.

[1]  Paul W. Goldberg,et al.  Learning unions of boxes with membership and equivalence queries , 1994, COLT '94.

[2]  Sally A. Goldman,et al.  Teaching a smart learner , 1993, COLT '93.

[3]  Dana Angluin,et al.  Learning with malicious membership queries and exceptions (extended abstract) , 1994, COLT '94.

[4]  Balas K. Natarajan,et al.  On learning Boolean functions , 1987, STOC.

[5]  Simon Kasif,et al.  Learning with a Helpful Teacher , 1991, IJCAI.

[6]  Michael Kearns,et al.  On the complexity of teaching , 1991, COLT '91.

[7]  Donna K. Slonim,et al.  Learning Monotone DNF with an Incomplete Membership Oracle , 1991, COLT.

[8]  Jeffrey C. Jackson,et al.  An efficient membership-query algorithm for learning DNF with respect to the uniform distribution , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[9]  Rusins Freivalds,et al.  On the Power of Inductive Inference from Good Examples , 1993, Theor. Comput. Sci..

[10]  Sampath Kannan,et al.  Oracles and queries that are sufficient for exact learning (extended abstract) , 1994, COLT '94.

[11]  Sampath Kannan,et al.  Oracles and Queries That Are Sufficient for Exact Learning , 1996, J. Comput. Syst. Sci..

[12]  Andrew Tomkins,et al.  A computational model of teaching , 1992, COLT '92.

[13]  Carl Smith,et al.  Testing Geometric Objects , 1994, Comput. Geom..

[14]  Sally A. Goldman,et al.  Teaching a Smarter Learner , 1996, J. Comput. Syst. Sci..

[15]  John Shawe-Taylor,et al.  On exact specification by examples , 1992, COLT '92.

[16]  György Turán,et al.  Learning with queries but incomplete information (extended abstract) , 1994, COLT '94.

[17]  Kathleen Romanik,et al.  Approximate testing and learnability , 1992, COLT '92.

[18]  Nader H. Bshouty,et al.  Exact learning via the Monotone theory , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[19]  Ronald L. Rivest,et al.  Learning Binary Relations and Total Orders , 1993, SIAM J. Comput..