The minimax optimal excess-risk rate for pure ε-DP heavy-tailed SCO is characterized up to logarithmic factors, with a polynomial-time algorithm based on Lipschitz extensions of the empirical loss and a nearly matching lower bound.
Privacy and statistical risk: Formalisms and minimax bounds
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Optimal Rates for Pure $\varepsilon$-Differentially Private Stochastic Convex Optimization with Heavy Tails
The minimax optimal excess-risk rate for pure ε-DP heavy-tailed SCO is characterized up to logarithmic factors, with a polynomial-time algorithm based on Lipschitz extensions of the empirical loss and a nearly matching lower bound.