Adversarial Risk and Robustness: General Definitions and Implications for the Uniform Distribution

As the current literature contains multiple definitions of a dversarial risk and robustness, we start by giving a taxonomy for these definitions based on their direct goals; we identify one of them as the one guaranteeing miscla ssification by pushing the instances to the error region . We then study some classic algorithms for learning monotone conjunctions and compare their adversar ial robustness under different definitions by attacking the hypotheses using ins tances drawn from the uniform distribution. We observe that sometimes these defin itions lead to significantly different bounds. Thus, this study advocates for the use of the error-r egion definition, even though other definitions, in other contexts with context-dependent assumptions, may coincide with the error-region definition .