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Relative deviation learning bounds and generalization with unbounded loss functions

Spencer Greenberg
Annals of Mathematics and Artificial Intelligence (2019)


We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of unbounded loss functions, under the assumption that a moment of the loss is bounded. We then illustrate how to apply these results in a sample application: the analysis of importance weighting.