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The Optimal Distribution-Free Sample Complexity of Distribution-Dependent Learning

This work establishes a new upper bound on the worst-case number of labeled samples sufficient for PAC learning in the realizable case, if the learning algorithm is allowed dependence on the data distribution, or an additional pool of unlabeled samples. The bound matches known lower bounds up to constant factors. This resolves a long-standing open problem on the sample complexity of distribution-dependent PAC learning. We also discuss potential avenues for extension to distribution-independent learning. The technique and analysis build on a recent breakthrough by Hans Simon.