Public-data Assisted Private Stochastic Optimization: Power and Limitations

arXiv:2403.03856v1 Announce Type: new
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 …

abstract algorithms arxiv big capability cs.cr cs.lg data delta epsilon focus limitations math.oc optimization power public public data risk show stat.ml stochastic study text type