← 研踪 PaperTrailarXiv:2611.04721 · v1
Pure Differentially Private Query Release via Laplace Input Smoothing
首次提交 2026-11-03 19:42
版本更新 2026-11-03 19:42
雷达观测 2026-11-04 23:39
摘要
We study the offline release of a public family of $k$ statistical queries on a database of $N$ records from a public universe of size $d$, under pure $\varepsilon$-differential privacy. We give an efficient algorithm that, with probability at least $1-β$, answers all queries simultaneously to error $$O\left(\min\left\{1,\sqrt{\frac{\log(d/β)\log k}{N\varepsilon}}\right\}\right).$$ The output is a synthetic histogram on the data universe, and its running time depends polynomially on $N,d$ and $k$. This resolves a conjecture of Nikolov and Ullman (2021) with an efficient, polynomial-time construction. Fitzsimons (2026) recently established the same square-root error scale via an information-theoretic construction that relies on a computationally intractable Lipschitz envelope over the exponential space of possible outputs. In contrast, we introduce an input-side smoothing approach: we run a selection-only multiplicative-weights process after a single sparse Laplace perturbation of the input histogram. Departing from standard first-order stability analyses, we investigate the stability of stability by establishing a uniform lower bound on the second-order log-derivatives of the output transcript across $T$ rounds of multiplicative weight updates. We then develop an analytic smoothing principle showing that this curvature bound allows a sparse, coordinate-wise perturbation to guarantee pure differential privacy globally, attaining optimal utility through a conceptually simple, polynomial-time pure-DP mechanism.
作者备注：35 pages
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v1 · 2026-11-03 19:42 · 最新观测版本
Pure Differentially Private Query Release via Laplace Input Smoothing
We study the offline release of a public family of $k$ statistical queries on a database of $N$ records from a public universe of size $d$, under pure $\varepsilon$-differential privacy. We give an efficient algorithm that, with probability at least $1-β$, answers all queries simultaneously to error $$O\left(\min\left\{1,\sqrt{\frac{\log(d/β)\log k}{N\varepsilon}}\right\}\right).$$ The output is a synthetic histogram on the data universe, and its running time depends polynomially on $N,d$ and $k$. This resolves a conjecture of Nikolov and Ullman (2021) with an efficient, polynomial-time construction. Fitzsimons (2026) recently established the same square-root error scale via an information-theoretic construction that relies on a computationally intractable Lipschitz envelope over the exponential space of possible outputs. In contrast, we introduce an input-side smoothing approach: we run a selection-only multiplicative-weights process after a single sparse Laplace perturbation of the input histogram. Departing from standard first-order stability analyses, we investigate the stability of stability by establishing a uniform lower bound on the second-order log-derivatives of the output transcript across $T$ rounds of multiplicative weight updates. We then develop an analytic smoothing principle showing that this curvature bound allows a sparse, coordinate-wise perturbation to guarantee pure differential privacy globally, attaining optimal utility through a conceptually simple, polynomial-time pure-DP mechanism.
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