Zeroth-order projected gradient descent without additive Gaussian noise is not differentially private in the worst case, and its privacy loss grows superlinearly with iterations.
In the fourth inequality, using the sec- ond property of the Cs-AC oracle, we get − PT j=1{Uj}i∗ ≥ 0, T ≥ 1
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On the Inherent Privacy of Zeroth Order Projected Gradient Descent
Zeroth-order projected gradient descent without additive Gaussian noise is not differentially private in the worst case, and its privacy loss grows superlinearly with iterations.