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# The Power of Random Counterexamples

*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.