论文标题
差异私人模型的更清晰的实用程序界限
Sharper Utility Bounds for Differentially Private Models
论文作者
论文摘要
在本文中，通过介绍广义的伯恩斯坦条件，我们提出了第一个$ \ Mathcal {o} \ big（\ frac {\ frac {\ sqrt {\ sqrt {p}} {nε} {nε} \ big）$高概率过多的人口过多的人口过多的人口过多的人口限制在假设下，以不同的私人算法限制了plusptions $ g $ lips $ lips $ lips-loak-loak-loak-loak-loak polothie and polotial liolak y。基于梯度扰动方法。如果我们替换属性$ g $ -lipschitz和$ l $ -smooth（$α$ -h {Ö} lder平滑度（可以在非平滑设置中使用），则高概率限制为$ \ Mathcal {o} {o} \ big big（n^{ - \fracα} $ \ nathcal {o} \ left（1/n \右）$当$α\ in（0,1] $。解决这个问题时，我们提出了梯度扰动方法的变体，\ textbf {max $ \ {1，g \ \} $ ngrigation formigition-fortimition formigition toblesition formigition formigition formigition timblediation fiors Show fiff strundiation。 $α$ -H {Ö} lder平滑而polyak-olojasiewicz条件可以达到$ \ nathcal {o} \ big（\ frac {\ sqrt {\ sqrt {p}} {nε} \ big）$，这是第一个$ \ nathcal prob {o} $ probition for tork for在非平滑条件下，我们评估了新提出的算法M-NGP的性能，实验结果表明，M-NGP改善了M-NGP的差异性模型。
In this paper, by introducing Generalized Bernstein condition, we propose the first $\mathcal{O}\big(\frac{\sqrt{p}}{nε}\big)$ high probability excess population risk bound for differentially private algorithms under the assumptions $G$-Lipschitz, $L$-smooth, and Polyak-Łojasiewicz condition, based on gradient perturbation method. If we replace the properties $G$-Lipschitz and $L$-smooth by $α$-H{ö}lder smoothness (which can be used in non-smooth setting), the high probability bound comes to $\mathcal{O}\big(n^{-\fracα{1+2α}}\big)$ w.r.t $n$, which cannot achieve $\mathcal{O}\left(1/n\right)$ when $α\in(0,1]$. To solve this problem, we propose a variant of gradient perturbation method, \textbf{max$\{1,g\}$-Normalized Gradient Perturbation} (m-NGP). We further show that by normalization, the high probability excess population risk bound under assumptions $α$-H{ö}lder smooth and Polyak-Łojasiewicz condition can achieve $\mathcal{O}\big(\frac{\sqrt{p}}{nε}\big)$, which is the first $\mathcal{O}\left(1/n\right)$ high probability excess population risk bound w.r.t $n$ for differentially private algorithms under non-smooth conditions. Moreover, we evaluate the performance of the new proposed algorithm m-NGP, the experimental results show that m-NGP improves the performance of the differentially private model over real datasets. It demonstrates that m-NGP improves the utility bound and the accuracy of the DP model on real datasets simultaneously.
