Non-Asymptotic Bounds for Adversarial Excess Risk under Misspecified Models

Autor:	Liu, Changyu, Jiao, Yuling, Wang, Junhui, Huang, Jian
Rok vydání:	2023
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning 62G05 62G08 68T07
Druh dokumentu:	Working Paper
Popis:	We propose a general approach to evaluating the performance of robust estimators based on adversarial losses under misspecified models. We first show 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, we study the adversarial excess risk. Our proposed analysis method includes investigations on both generalization error and approximation error. We then establish non-asymptotic upper bounds for the adversarial excess risk associated with Lipschitz loss functions. In addition, we apply our general results to adversarial training for classification and regression problems. For the quadratic loss in nonparametric regression, we show that the adversarial excess risk bound can be improved over those for a general loss. Comment: 27 pages, 3 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.00771 Zobrazit plný text záznamu View this record from Arxiv