Differentially-Private Collaborative Online Personalized Mean Estimation

We consider the problem of collaborative personalized mean estimation under a privacy constraint in an environment of several agents continuously receiving data according to arbitrary unknown agent-specific distributions. In particular, we provide a method based on hypothesis testing coupled with differential privacy and data variance estimation. Two privacy mechanisms and two data variance estimation schemes are proposed, and we provide a theoretical convergence analysis of the proposed algorithm for any bounded unknown distributions on the agents' data, showing that collaboration provides faster convergence than a fully local approach where agents do not share data. Moreover, we provide analytical performance curves for the case with an oracle class estimator, i.e., the class structure of the agents, where agents receiving data from distributions with the same mean are considered to be in the same class, is known. The theoretical faster-than-local convergence guarantee is backed up by extensive numerical results showing that for a considered scenario the proposed approach indeed converges much faster than a fully local approach, and performs comparably to ideal performance where all data is public. This illustrates the benefit of private collaboration in an online setting.

Straggler-Resilient Differentially-Private Decentralized Learning

We consider the straggler problem in decentralized learning over a logical ring while preserving user data privacy. Especially, we extend the recently proposed framework of differential privacy (DP) amplification by decentralization by Cyffers and Bellet to include overall training latency--comprising both computation and communication latency. Analytical results on both the convergence speed and the DP level are derived for both a skipping scheme (which ignores the stragglers after a timeout) and a baseline scheme that waits for each node to finish before the training continues. A trade-off between overall training latency, accuracy, and privacy, parameterized by the timeout of the skipping scheme, is identified and empirically validated for logistic regression on a real-world dataset.

Pliable Private Information Retrieval

We formulate a new variant of the private information retrieval (PIR) problem where the user is pliable, i.e., interested in any message from a desired subset of the available dataset, denoted as pliable private information retrieval (PPIR). We consider a setup where a dataset consisting of $f$ messages is replicated in $n$ noncolluding databases and classified into $\Gamma$ classes. For this setup, the user wishes to retrieve any $\lambda\geq 1$ messages from multiple desired classes, i.e., $\eta\geq 1$, while revealing no information about the identity of the desired classes to the databases. We term this problem multi-message PPIR (M-PPIR) and introduce the single-message PPIR (PPIR) problem as an elementary special case of M-PPIR. We first derive converse bounds on the M-PPIR rate, which is defined as the ratio of the desired amount of information and the total amount of downloaded information, followed by the corresponding achievable schemes. As a result, we show that the PPIR capacity, i.e., the maximum achievable PPIR rate, for $n$ noncolluding databases matches the capacity of PIR with $n$ databases and $\Gamma$ messages. Thus, enabling flexibility, i.e., pliability, where privacy is only guaranteed for classes, but not for messages as in classical PIR, allows to trade-off privacy versus download rate. A similar insight is shown to hold for the general case of M-PPIR.