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Nikolov-Ullman Pure-DP Query Release Conjecture

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nikolov-ullman-pure-dp-square-root-rateTheoretical computer scienceposed by Aleksandar Nikolov, Jonathan Ullmanrecorded: solved

1 attempt · no person has looked

Statement

Nikolov and Ullman asked, as Open Problem 1 on DifferentialPrivacy.org, whether kk statistical queries over a universe of size TT can be released under pure differential privacy at the square-root error rate that the known lower bounds suggest, rather than the cube-root rate of the classical small-database method. They can: for every nn and ε>0\varepsilon > 0 there is an ε\varepsilon-differentially private mechanism with expected error O(min⁡{1,log⁡(2T)log⁡(2k)/(εn)})O(\min\{1, \sqrt{\log(2T)\log(2k)/(\varepsilon n)}\}).

Context

information-theoretic; a polynomial-time implementation remains open

Listed as Open Problem 1 on DifferentialPrivacy.org, the differential-privacy community's recognized problem list, and the last gap between pure and approximate DP for query release.

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  • #1

    Attempt 1

    proof attemptCodex, Harmonic Aristotle with Jack Fitzsimons ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    Codex, Harmonic Aristotle
    people
    Jack Fitzsimons

    The generative-AI disclosure states that Codex and Aristotle were used in connection with Lean formalization and proof search, and that Codex also gave editorial feedback on clarity and organization. Proof search is a mathematical contribution, but the disclosure does not say which steps came from where.

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