Efficient derandomization of differentially private counting queries
Surendra Ghentiyala
TL;DR
The paper tackles the high randomness costs of differential privacy for counting queries by introducing a polynomial-time, derandomized mechanism that achieves near-optimal randomness-accuracy tradeoffs for both approximate and pure DP. Central to the approach is a randomized shifting technique that causes many coordinates to become noise-insensitive, enabling selective noise addition and avoiding extensive rounding schemes. The authors provide explicit complexity and accuracy bounds, showing randomness usage of the form $R(\mathcal{M}) = O\left( \frac{d}{s} \mathrm{polylog}(d/\varepsilon) + \log s \right)$ (pure DP) and $R_0(\mathcal{M}) = O\left( \log d + \log(1/\delta) \right)$ (approx DP under certain parameter regimes), with polynomial-time running and provable $(\varepsilon,\delta)$-DP or $(\varepsilon,0)$-DP guarantees and corresponding accuracy $\alpha$. A key contribution is a constructive, efficient mechanism family (Mechanisms 1–5) that leverages discrete Gaussian and discrete Laplace noise, stratified sampling, and a rounding scheme tied to a coarse grid to achieve randomness savings while preserving privacy. The work also presents a general result for sampling from efficiently approximable discrete distributions, enabling practical implementation of the proposed derandomization. Overall, the paper significantly reduces the randomness required for private counting queries and provides a clear, implementable path toward randomness-efficient DP in large-scale data settings.
Abstract
Differential privacy for the 2020 census required an estimated 90 terabytes of randomness [GL20], an amount which may be prohibitively expensive or entirely infeasible to generate. Motivated by these practical concerns, [CSV25] initiated the study of the randomness complexity of differential privacy, and in particular, the randomness complexity of $d$ counting queries. This is the task of outputting the number of entries in a dataset that satisfy predicates $\mathcal{P}_1, \dots, \mathcal{P}_d$ respectively. They showed the rather surprising fact that though any reasonably accurate, $\varepsilon$-differentially private mechanism for one counting query requires $1-O(\varepsilon)$ bits of randomness in expectation, there exists a fairly accurate mechanism for $d$ counting queries which requires only $O(\log d)$ bits of randomness in expectation. The mechanism of [CSV25] is inefficient (not polynomial time) and relies on a combinatorial object known as rounding schemes. Here, we give a polynomial time mechanism which achieves nearly the same randomness complexity versus accuracy tradeoff as that of [CSV25]. Our construction is based on the following simple observation: after a randomized shift of the answer to each counting query, the answer to many counting queries remains the same regardless of whether we add noise to that coordinate or not. This allows us to forgo the step of adding noise to the result of many counting queries. Our mechanism does not make use of rounding schemes. Therefore, it provides a different -- and, in our opinion, clearer -- insight into the origins of the randomness savings that can be obtained by batching $d$ counting queries.