Adaptive Data Analysis in a Balanced Adversarial Model

Kobbi Nissim, Uri Stemmer, Eliad Tsfadia

Research output: Contribution to journalConference articlepeer-review

Abstract

In adaptive data analysis, a mechanism gets n i.i.d. samples from an unknown distribution D, and is required to provide accurate estimations to a sequence of adaptively chosen statistical queries with respect to D. Hardt and Ullman [2014] and Steinke and Ullman [2015a] showed that, in general, it is computationally hard to answer more than Θ(n2) adaptive queries, assuming the existence of one-way functions. However, these negative results strongly rely on an adversarial model that significantly advantages the adversarial analyst over the mechanism, as the analyst, who chooses the adaptive queries, also chooses the underlying distribution D. This imbalance raises questions with respect to the applicability of the obtained hardness results - an analyst who has complete knowledge of the underlying distribution D would have little need, if at all, to issue statistical queries to a mechanism which only holds a finite number of samples from D. We consider more restricted adversaries, called balanced, where each such adversary consists of two separate algorithms: The sampler who is the entity that chooses the distribution and provides the samples to the mechanism, and the analyst who chooses the adaptive queries, but has no prior knowledge of the underlying distribution (and hence has no a priori advantage with respect to the mechanism). We improve the quality of previous lower bounds by revisiting them using an efficient balanced adversary, under standard public-key cryptography assumptions. We show that these stronger hardness assumptions are unavoidable in the sense that any computationally bounded balanced adversary that has the structure of all known attacks, implies the existence of public-key cryptography.

Original languageEnglish
JournalAdvances in Neural Information Processing Systems
Volume36
StatePublished - 2023
Event37th Conference on Neural Information Processing Systems, NeurIPS 2023 - New Orleans, United States
Duration: 10 Dec 202316 Dec 2023

Funding

FundersFunder number
Blavatnik Family Foundation
National Science FoundationCNS-2001041
National Science Foundation
Israel Science Foundation1871/19
Israel Science Foundation

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