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Generalization error boundaries are essential for comprehending how wellmachine learning models work. In this work, we suggest a creative method, i.e.,the Auxiliary Distribution Method, that derives new upper bounds ongeneralization errors that are appropriate for supervised learning scenarios.We show that our general upper bounds can be specialized under some conditionsto new bounds involving the generalized $\alpha$-Jensen-Shannon,$\alpha$-R\'enyi ($0< \alpha < 1$) information between random variable modelingthe set of training samples and another random variable modeling the set ofhypotheses. Our upper bounds based on generalized $\alpha$-Jensen-Shannoninformation are also finite. Additionally, we demonstrate how our auxiliarydistribution method can be used to derive the upper bounds on generalizationerror under the distribution mismatch scenario in supervised learningalgorithms, where the distributional mismatch is modeled as$\alpha$-Jensen-Shannon or $\alpha$-R\'enyi ($0< \alpha < 1$) between thedistribution of test and training data samples. We also outline thecircumstances in which our proposed upper bounds might be tighter than otherearlier upper bounds.

Learning Algorithm Generalization Error Bounds via Auxiliary Distributions