Adversarially robust estimators transfer to heavy-tailed estimation for free, but heavy-tailed estimators do not transfer back to adversarial contamination.
Concentration Inequalities and Empirical Processes Theory Applied to the Analysis of Learning Algorithms
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Heavy-tailed Contamination is Easier than Adversarial Contamination
Adversarially robust estimators transfer to heavy-tailed estimation for free, but heavy-tailed estimators do not transfer back to adversarial contamination.