Albert Cheu — Page 2

arXiv2019

Distributed Differential Privacy via Shuffling

We consider the problem of designing scalable, robust protocols for computing statistics about sensitive data. Specifically, we look at how best to design differentially private protocols in a distributed setting, where each user holds a private datum. The literature has mostly considered two models: the "central" model, in which a trusted server collects users' data in the clear, which allows greater accuracy; and the "local" model, in which users individually randomize their data, and need not trust the server, but accuracy is limited. Attempts to achieve the accuracy of the central model without a trusted server have so far focused on variants of cryptographic MPC, which limits scalability. In this paper, we initiate the analytic study of a shuffled model for distributed differentially private algorithms, which lies between the local and central models. This simple-to-implement model, a special case of the ESA framework of [Bittau et al., '17], augments the local model with an anonymous channel that randomly permutes a set of user-supplied messages. For sum queries, we show that this model provides the power of the central model while avoiding the need to trust a central server and the complexity of cryptographic secure function evaluation. More generally, we give evidence that the power of the shuffled model lies strictly between those of the central and local models: for a natural restriction of the model, we show that shuffled protocols for a widely studied selection problem require exponentially higher sample complexity than do central-model protocols.

cs.CR↗

arXiv2018

Skyline Identification in Multi-Armed Bandits

We introduce a variant of the classical PAC multi-armed bandit problem. There is an ordered set of $n$ arms $A[1],\dots,A[n]$, each with some stochastic reward drawn from some unknown bounded distribution. The goal is to identify the $skyline$ of the set $A$, consisting of all arms $A[i]$ such that $A[i]$ has larger expected reward than all lower-numbered arms $A[1],\dots,A[i-1]$. We define a natural notion of an $\varepsilon$-approximate skyline and prove matching upper and lower bounds for identifying an $\varepsilon$-skyline. Specifically, we show that in order to identify an $\varepsilon$-skyline from among $n$ arms with probability $1-δ$, $$ Θ\bigg(\frac{n}{\varepsilon^2} \cdot \min\bigg\{ \log\bigg(\frac{1}{\varepsilon δ}\bigg), \log\bigg(\frac{n}δ\bigg) \bigg\} \bigg) $$ samples are necessary and sufficient. When $\varepsilon \gg 1/n$, our results improve over the naive algorithm, which draws enough samples to approximate the expected reward of every arm; the algorithm of (Auer et al., AISTATS'16) for Pareto-optimal arm identification is likewise superseded. Our results show that the sample complexity of the skyline problem lies strictly in between that of best arm identification (Even-Dar et al., COLT'02) and that of approximating the expected reward of every arm.

cs.LG↗