Simple Algorithms for Learning from Random Counterexamples
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This work describes two simple and efficient algorithms for exactly learning a target concept from a finite n × m concept space, in the setting where the teacher draws counter-examples randomly from some known probability distribution. The first learning algorithm guarantees that the learner will only need to see O(n) counter-examples, in expectation, to identify the target concept. The second algorithm is applicable to the case where the teacher also draws their target concept at the beginning of the learning process from a different known probability distribution. Even for this case, we show that the learner can still identify the target concept after only seeing O(n) counter-examples, in expectation, by simply drawing their hypothesis randomly from the known teacher's distribution conditioned on the previously revealed counter-examples.
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