Introduces hybrid noise and novel coupling analysis to achieve the first convergent hidden-state DP bound for zeroth-order optimization.
Since W1 (d) = Z2 for Z ∼ N (0, 1), by the lower bound of the Q-function, it holds that P {W1 ≥ κ1} = P {|Z| ≥ √κ1} = 2 · Q (√κ1) ≥ √κ1 1 + κ1 e−κ1/2 √ 2π
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Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States
Introduces hybrid noise and novel coupling analysis to achieve the first convergent hidden-state DP bound for zeroth-order optimization.