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.
Then E PN j=1{Uj}i∗ 2 ≤ CsE hPN j=1{Uj}i∗ i2 Theorem C.2
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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.