On Proper Learnability between Average- and Worst-case Robustness
This addresses the challenge of enabling proper learning in robust machine learning for researchers, though it appears incremental as it builds on prior hardness results.
The paper tackles the problem of proper learnability in adversarially robust PAC learning by studying relaxations of worst-case robust loss, showing that VC classes are properly learnable under certain relaxations with sample complexity close to standard PAC learning, but not under an existing natural relaxation.
Recently, Montasser et al. [2019] showed that finite VC dimension is not sufficient for proper adversarially robust PAC learning. In light of this hardness, there is a growing effort to study what type of relaxations to the adversarially robust PAC learning setup can enable proper learnability. In this work, we initiate the study of proper learning under relaxations of the worst-case robust loss. We give a family of robust loss relaxations under which VC classes are properly PAC learnable with sample complexity close to what one would require in the standard PAC learning setup. On the other hand, we show that for an existing and natural relaxation of the worst-case robust loss, finite VC dimension is not sufficient for proper learning. Lastly, we give new generalization guarantees for the adversarially robust empirical risk minimizer.