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 Computational Learning Theory




db6461eaf0eaeaad1d9c4a70e4818cbd-Supplemental-Conference.pdf

Neural Information Processing Systems

Distributional assumptions have been shown to be necessary for the robust learn-ability of concept classes when considering the exact-in-the-ball robust risk and access to random examples by Gourdeau et al. (2019).


db6461eaf0eaeaad1d9c4a70e4818cbd-Paper-Conference.pdf

Neural Information Processing Systems

Distributional assumptions have been shown to be necessary for the robust learn-ability of concept classes when considering the exact-in-the-ball robust risk and access to random examples by Gourdeau et al. (2019).





Supplementary Material A Proof of Theorem 3.1 (Realizable Case - Positive Result) Theorem (Restatement of Theorem 3.1)

Neural Information Processing Systems

Let H be a hypothesis class with VC dimension d and let 2 (0, 1) . Then there exists a learner Lrn having -adversarial risk " To prove Theorem 3.1, we will use the S SPV and let n 1 / be the sample size. By applying linearity of expectation we get E " 1 t To prove Theorem 3.1, we will need an optimal learner as an input learner for SPV . Theorem 3.1 can now be immediately inferred as a direct application of Lemma A.1 and Theorem A.2 . The impossibility result in Theorem 3.3 extends to randomized learning rules.