Relative Deviation Margin Bounds

We present a series of new and more favorable margin-based learning guarantees that depend on the empirical margin loss of a predictor. We give two types of learning bounds, both distribution-dependent and valid for general families, in terms of the Rademacher complexity or the empirical $ell_infty$ covering number of the hypothesis set used. Furthermore, using our relative deviation margin bounds, we derive distribution-dependent generalization bounds for unbounded loss functions under the assumption of a finite moment. We also briefly highlight several applications of these bounds and discuss their connection with existing results.