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.
Using, the second property of Cs-AC oracle, we have Z = − PT j=1{Uj}i∗ ≥ 0
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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.