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Bounding the generalization error of a supervised learning algorithm is oneof the most important problems in learning theory, and various approaches havebeen developed. However, existing bounds are often loose and lack ofguarantees. As a result, they may fail to characterize the exact generalizationability of a learning algorithm. Our main contribution is an exactcharacterization of the expected generalization error of the well-known Gibbsalgorithm in terms of symmetrized KL information between the input trainingsamples and the output hypothesis. Such a result can be applied to tightenexisting expected generalization error bound. Our analysis provides moreinsight on the fundamental role the symmetrized KL information plays incontrolling the generalization error of the Gibbs algorithm.

Characterizing the Generalization Error of Gibbs Algorithm with Symmetrized KL information