A Rate Separation for Agnostic Direct Sums

Hanneke, Moran, and Waknine citeHannekeMoranWaknine2024 asked how the agnostic PAC learning curve of the direct sum Cr depends on the single-instance learning curve epsagn(nmid C) and on r. We show that the single-instance learning rate does not determine the direct-sum rate. Let F be the class of the two constant binary functions and let G consist of the zero function and the identity function. Both classes have agnostic learning curve of order n-1/2.