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Register a new userThe Role of Interactivity in Local Differential Privacy
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Matthew Joseph
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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We study the power of interactivity in local differential privacy. First, we focus on the difference between fully interactive and sequentially interactive protocols. Sequentially interactive protocols may query users adaptively in sequence, but they cannot return to previously queried users. The vast majority of existing lower bounds for local differential privacy apply only to sequentially interactive protocols, and before this paper it was not known whether fully interactive protocols were more powerful. We resolve this question. First, we classify locally private protocols by their compositionality, the multiplicative factor $k geq 1$ by which the sum of a protocols single-round privacy parameters exceeds its overall privacy guarantee. We then show how to efficiently transform any fully interactive $k$-compositional protocol into an equivalent sequentially interactive protocol with an $O(k)$ blowup in sample complexity. Next, we show that our reduction is tight by exhibiting a family of problems such that for any $k$, there is a fully interactive $k$-compositional protocol which solves the problem, while no sequentially interactive protocol can solve the problem without at least an $tilde Omega(k)$ factor more examples. We then turn our attention to hypothesis testing problems. We show that for a large class of compound hypothesis testing problems --- which include all simple hypothesis testing problems as a special case --- a simple noninteractive test is optimal among the class of all (possibly fully interactive) tests.
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We prove a general connection between the communication complexity of two-player games and the sample complexity of their multi-player locally private analogues. We use this connection to prove sample complexity lower bounds for locally differentially private protocols as straightforward corollaries of results from communication complexity. In particular, we 1) use a communication lower bound for the hidden layers problem to prove an exponential sample complexity separation between sequentially and fully interactive locally private protocols, and 2) use a communication lower bound for the pointer chasing problem to prove an exponential sample complexity separation between $k$ round and $k+1$ round sequentially interactive locally private protocols, for every $k$.
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