CORTEXA
← Browse
arxivcs.DScs.CRcs.LG2026-07-01

The Binary Tree Mechanism is Optimal for Approximate Differentially Private Continual Counting

Konstantina Bairaktari, Kasper Green Larsen

Private continual counting is a fundamental problem in differential privacy: given a binary stream of length $n$, where each $1$ corresponds to the contribution of one individual, the goal is to release all running counts while protecting the privacy of each individual. The standard algorithm is the binary tree mechanism, whose Gaussian-noise variant achieves expected $\ell_\infty$ error proportional to $\log^{3/2} n$ for approximate differential privacy. Whether this dependence on the stream length is necessary has remained a central open problem. In this work, we resolve the dependence on $n$ by proving that every differentially private mechanism for continual counting must incur expected $\ell_\infty$ error $Ω(\log^{3/2} n)$. This shows that the binary tree mechanism is asymptotically optimal in the approximate-DP setting. As a consequence, we also obtain a largest-possible separation between hereditary discrepancy and private $\ell_\infty$ error for linear queries, showing that the known general upper bound in terms of hereditary discrepancy has the optimal dependence on the number of queries.

View free PDFSource page

Related papers

arxivcs.CRcs.DScs.LG2026-07-08

Is Randomness Necessary for Adaptive Data Analysis?

Edith Cohen, Haim Kaplan, Yishay Mansour, Shay Sapir, Uri Stemmer

The Adaptive Data Analysis (ADA) problem formalizes the challenge of preventing false discovery and overfitting when a dataset is repeatedly reused. Formally, our input is a dataset containing $n$ i.i.d.\ samples from an unknown distribution $P$ over a domain $X$, and our goal is…

View free PDFSource page
arxivcs.CRcs.LG2026-07-03

Scalable Differentially Private Data Compression via Diffusion and Stochastic Codes

Gergely Flamich, Oykü Sıla Güner, Yanxiao Liu, Deniz Gündüz

The ever-increasing collection of personal data has created mounting pressure to develop technologies that protect sensitive aspects of individual identity. Differential privacy (DP) provides a principled framework with strong formal guarantees and has already achieved practical…

View free PDFSource page
arxivcs.LGcs.AIcs.CRcs.CY2026-07-18

Privacy Cost as Equity Input: A Group Fairness Criterion for Differentially Private Machine Learning

Rakshit Naidu

Differential privacy (DP) is increasingly deployed to limit membership inference risk in machine-learning systems. Prior work has shown that DP-SGD can widen accuracy disparities across demographic groups, but this framing treats fairness as a purely outcome-side concern. We argu…

View free PDFSource page
arxivcs.LGcs.AIcs.CR2026-07-08

Where to Intervene? Benchmarking Fairness-Aware Learning on Differentially Private Synthetic Tabular Data

Vinícius Gabriel Angelozzi, Héber H. Arcolezi

Machine learning models are increasingly deployed in high-stakes domains, raising concerns about both privacy and fairness. Differential Privacy (DP) has become a gold standard for privacy-preserving data analysis, while fairness-aware mechanisms aim to mitigate discrimination ag…

View free PDFSource page