Relative Deviation Margin Bounds

@InProceedings{pmlr-v139-cortes21a,
  title = 	 {Relative Deviation Margin Bounds},
  author =       {Cortes, Corinna and Mohri, Mehryar and Suresh, Ananda Theertha},
  booktitle = 	 {Proceedings of the 38th International Conference on Machine Learning},
  pages = 	 {2122--2131},
  year = 	 {2021},
  editor = 	 {Meila, Marina and Zhang, Tong},
  volume = 	 {139},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {18--24 Jul},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v139/cortes21a/cortes21a.pdf},
  url = 	 {https://proceedings.mlr.press/v139/cortes21a.html},
  abstract = 	 {We present a series of new and more favorable margin-based learning guarantees that depend on the empirical margin loss of a predictor. e give two types of learning bounds, in terms of either the Rademacher complexity or the empirical $\ell_\infty$-covering number of the hypothesis set used, both distribution-dependent and valid for general families. 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.}
}