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Differentially Private Online-to-Batch for Smooth Losses
Qinzi Zhang, Hoang Tran, Ashok Cutkosky · 2022-10-13 · via cs.LG updates on arXiv.org

We develop a new reduction that converts any online convex optimization algorithm suffering $O(\sqrt{T})$ regret into an $ε$-differentially private stochastic convex optimization algorithm with the optimal convergence rate $\tilde O(1/\sqrt{T} + \sqrt{d}/εT)$ on smooth losses in linear time, forming a direct analogy to the classical non-private "online-to-batch" conversion. By applying our techniques to more advanced adaptive online algorithms, we produce adaptive differentially private counterparts whose convergence rates depend on apriori unknown variances or parameter norms.

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