In the testable learning model, the learning algorithm, or tester-learner, is given access to labeled examples from an unknown distribution and may either reject or accept the unknown distribution. If it accepts, it must successfully produce a near-optimal hypothesis.

Adversarial robustness is an increasingly critical property of classifiers in applications. The design of robust algorithms relies on surrogate losses since the optimization of the adversarial loss with most hypothesis sets is NP-hard.

The widely studiedGeneralized Min-Sum-Set-Cover(GMSSC) problem serves as a formal model for the setting above. GMSSC is NP-hard and the standard application ofno-regretonline learning algorithms iscomputationally inefficient, because they operate in the space of rankings. In this work, we show how to achievelowregret for GMSSC inpolynomial-time.

Inparticular[25] present show generalization Pr competition 26] sought given generalization Theparticipants32,40,48] achie VC-dimension 54] and 4].