The Price of Differential Privacy under Continual Observation

Palak Jain, Sofya Raskhodnikova, Satchit Sivakumar, Adam Smith

TPDP 2022

Satchit and me with our TPDP poster at Graffiti Alley in Baltimore, Maryland.

We study the accuracy of differentially private mechanisms in the continual release model. A continual release mechanism receives a sensitive dataset as a stream of T inputs and produces, after receiving each input, an output that is accurate for all the inputs received so far.
In contrast, a batch algorithm receives the data as one batch and produces a single output.

We provide the first strong lower bounds on the error of continual release mechanisms. In particular, for two fundamental problems that are widely studied and used in the batch model, we show that the worst case error of every continual release algorithm is  Ω̃ (T^1/3) times larger than that of the best batch algorithm. Previous work shows only a polylogarithimic (in T) gap between the worst case error achievable in these two models; further, for many problems, including the summation of binary attributes, the polylogarithmic gap is tight (Dwork et al., 2010; Chan et al., 2010). Our results show that problems closely related to summation—specifically, those that require selecting the largest of a set of sums—are fundamentally harder in the continual release model than in the batch model.

Our lower bounds assume only that privacy holds for streams fixed in advance (the “nonadaptive” setting). We also formulate a model that allows for adaptively selected inputs and prove the privacy of several known algorithms in that model. In particular we show that our lower bounds are matched by the error of simple algorithms whose privacy holds even for adaptively selected streams. The adaptive model captures dependencies that arise in many applications of continual release.

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