Evaluation May Be Easier Than Generation

Moni Naor


Kearns et al. (STOC 94) defined two notions for learning a distribution D. The first is with a generator, where the learner presents a generator that outputs a distribution identical or close to D. The other is with an evaluator, where the learner presents a procedure that on input x evaluates correctly (or approximates) the probability that x is generated by D. They showed an example where efficient learning by a generator is possible, but learning by an evaluator is computationally infeasible.

Though it may seem that generation is, in general, easier than evaluation, in this talk we show that the converse may be true: we provide a class of distributions where efficient learning with an evaluator is possible, but coming up with a generator that approximates the given distribution is infeasible. We also show that some distributions may be learned (with either a generator or an evaluator) to within any epsilon > 0, but the learned hypothesis must be of size proportional to epsilon (and not log epsilon which is always the case in the distribution-free PAC model).

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