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12151_differentially_private_general.pdf

Neural Information Processing Systems

A.3 Low Dimension Before presenting the proof of Theorem 1, we provide formal statements of its Corollaries. We then bound average argument stability in terms of average regret (Lemma 5). Substituting these in the above equation gives the claimed bound. We now fill in the details. Thus, substituting the above in Eqn. ( 3) and substituting the bound from 6, we have, E [ L ( null w; D) L ( w Substituting the value of G completes the proof.