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Public-data Assisted Private Stochastic Optimization: Power and Limitations
March 7, 2024, 5:11 a.m. | Enayat Ullah, Michael Menart, Raef Bassily, Crist\'obal Guzm\'an, Raman Arora
cs.CR updates on arXiv.org arxiv.org
Abstract: We study the limits and capability of public-data assisted differentially private (PA-DP) algorithms. Specifically, we focus on the problem of stochastic convex optimization (SCO) with either labeled or unlabeled public data. For complete/labeled public data, we show that any $(\epsilon,\delta)$-PA-DP has excess risk $\tilde{\Omega}\big(\min\big\{\frac{1}{\sqrt{n_{\text{pub}}}},\frac{1}{\sqrt{n}}+\frac{\sqrt{d}}{n\epsilon} \big\} \big)$, where $d$ is the dimension, ${n_{\text{pub}}}$ is the number of public samples, ${n_{\text{priv}}}$ is the number of private samples, and $n={n_{\text{pub}}}+{n_{\text{priv}}}$. These lower bounds are established via our new …
algorithms arxiv big cs.cr cs.lg data delta excess focus limitations math.oc omega optimization power private problem public risk sco stat.ml study text
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