A0949
Title: Non-asymptotic bounds for adversarial excess risk under misspecified models
Authors: Changyu Liu - Department of Statistics, The Chinese University of Hong Kong (Hong Kong) [presenting]
Abstract: The aim is to propose a general approach to evaluating the performance of robust estimators based on adversarial losses under misspecified models. It is first shown that adversarial risk is equivalent to the risk induced by a distributional adversarial attack under certain smoothness conditions. This ensures that the adversarial training procedure is well-defined. To evaluate the generalization performance of the adversarial estimator, the adversarial excess risk is studied. The proposed analysis method includes investigations on both generalization error and approximation error. Non-asymptotic upper bounds are then established for the adversarial excess risk associated with Lipschitz loss functions. In addition, the general results are applied to adversarial training for classification and regression problems. For the quadratic loss in nonparametric regression, it is shown that the adversarial excess risk bound can be improved over those for a general loss.
