DP-SCO with Tsybakov noise and bounded gradient moments is claimed to achieve excess risk ((r(1/sqrt(n)+sqrt(d)/(n eps))^{(k-1)/k}))^{theta/(theta-1)} with high probability, but the lower bound proof violates the paper's own moment assumption.
Differentially private assouad, fano, and le cam
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Beyond Ordinary Lipschitz Constraints: Differentially Private Stochastic Optimization with Tsybakov Noise Condition
DP-SCO with Tsybakov noise and bounded gradient moments is claimed to achieve excess risk ((r(1/sqrt(n)+sqrt(d)/(n eps))^{(k-1)/k}))^{theta/(theta-1)} with high probability, but the lower bound proof violates the paper's own moment assumption.