In recent years, the analysis of max-lp-margin classifiers has gained attention from the theory community not only due to the implicit bias of first-order methods, but also due to the observation of harmless interpolation for neural networks. In this talk, I will discuss two results: We show that surprisingly, in the noiseless case, while minimizing the l1-norm achieves optimal rates for regression for hard-sparse ground truths, this adaptivity does not directly apply to the equivalent of max l1-margin classification. Further, for noisy observations, we prove how max-lp-margin classifiers can achieve 1/\sqrt{n} rates for p slightly larger than one, while the maximum l1-margin classifier only achieves rates of order 1/sqrt(log(d/n)).
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