The Power of Random Counterexamples

Dana Angluin; Tyler Dohrn

The Power of Random Counterexamples

Dana Angluin, Tyler Dohrn ;

Proceedings of the 28th International Conference on Algorithmic Learning Theory, PMLR 76:452-465, 2017.

Abstract

Learning a target concept from a finite $n \times m$ concept space requires $\Omega{(n)}$ proper equivalence queries in the worst case. We propose a variation of the usual equivalence query in which the teacher is constrained to choose counterexamples randomly from a known probability distribution on examples. We present and analyze the Max-Min learning algorithm, which identifies an arbitrary target concept in an arbitrary finite $n \times m$ concept space using at most an expected $\log_2{n}$ proper equivalence queries with random counterexamples.

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@InProceedings{pmlr-v76-angluin17a, title = {The Power of Random Counterexamples}, author = {Dana Angluin and Tyler Dohrn}, booktitle = {Proceedings of the 28th International Conference on Algorithmic Learning Theory}, pages = {452--465}, year = {2017}, editor = {Steve Hanneke and Lev Reyzin}, volume = {76}, series = {Proceedings of Machine Learning Research}, address = {Kyoto University, Kyoto, Japan}, month = {15--17 Oct}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v76/angluin17a/angluin17a.pdf}, url = {http://proceedings.mlr.press/v76/angluin17a.html}, abstract = {Learning a target concept from a finite $n \times m$ concept space requires $\Omega{(n)}$ proper equivalence queries in the worst case. We propose a variation of the usual equivalence query in which the teacher is constrained to choose counterexamples randomly from a known probability distribution on examples. We present and analyze the Max-Min learning algorithm, which identifies an arbitrary target concept in an arbitrary finite $n \times m$ concept space using at most an expected $\log_2{n}$ proper equivalence queries with random counterexamples.} }

%0 Conference Paper %T The Power of Random Counterexamples %A Dana Angluin %A Tyler Dohrn %B Proceedings of the 28th International Conference on Algorithmic Learning Theory %C Proceedings of Machine Learning Research %D 2017 %E Steve Hanneke %E Lev Reyzin %F pmlr-v76-angluin17a %I PMLR %J Proceedings of Machine Learning Research %P 452--465 %U http://proceedings.mlr.press %V 76 %W PMLR %X Learning a target concept from a finite $n \times m$ concept space requires $\Omega{(n)}$ proper equivalence queries in the worst case. We propose a variation of the usual equivalence query in which the teacher is constrained to choose counterexamples randomly from a known probability distribution on examples. We present and analyze the Max-Min learning algorithm, which identifies an arbitrary target concept in an arbitrary finite $n \times m$ concept space using at most an expected $\log_2{n}$ proper equivalence queries with random counterexamples.