We study the problem of maintaining a differentially private decaying sum under continual observation. We give a unifying framework and an efficient algorithm for this problem for \emph{any sufficiently smooth} function. Our algorithm is the first differentially private algorithm that does not have a multiplicative error for polynomially-decaying weights. Our algorithm improves on all prior works on differentially private decaying sums under continual observation and recovers exactly the additive error for the special case of continual counting from Henzinger et al. (SODA 2023) as a corollary.
Our algorithm is a variant of the factorization mechanism whose error depends on the $γ_2$ and $γ_F$ norm of the underlying matrix. We give a constructive proof for an almost exact upper bound on the $γ_2$ and $γ_F$ norm and an almost tight lower bound on the $γ_2$ norm for a large class of lower-triangular matrices. This is the first non-trivial lower bound for lower-triangular matrices whose non-zero entries are not all the same. It includes matrices for all continual decaying sums problems, resulting in an upper bound on the additive error of any differentially private decaying sums algorithm under continual observation.
We also explore some implications of our result in discrepancy theory and operator algebra. Given the importance of the $γ_2$ norm in computer science and the extensive work in mathematics, we believe our result will have further applications.
Catastrophic forgetting can be a significant problem for institutions that must delete historic data for privacy reasons. For example, hospitals might not be able to retain patient data permanently. But neural networks trained on recent data alone will tend to forget lessons learned on old data. We present a differentially private continual learning framework based on variational inference. We estimate the likelihood of past data given the current model using differentially private generative models of old datasets.
Almost Tight Error Bounds on Differentially Private Continual Counting
Faculty of Computer Science, University of Vienna（维也纳大学计算机学院）；Rutgers University（罗格斯大学）；Indian Statistical Institute, Delhi（印度统计研究所德里中心）；Fujitsu Research of America（美国富士通研究所）
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Indian Institute of Science, Bangalore（印度科学学院班加罗尔分院）
We consider the problem of continually releasing an estimate of the population mean of a stream of samples that is user-level differentially private (DP). At each time instant, a user contributes a sample, and the users can arrive in arbitrary order. Until now these requirements of continual release and user-level privacy were considered in isolation. But, in practice, both these requirements come together as the users often contribute data repeatedly and multiple queries are made. We provide an algorithm that outputs a mean estimate at every time instant $t$ such that the overall release is u…
Google Research（谷歌研究院）；Tel Aviv University（特拉维夫大学）
We introduce the concurrent shuffle model of differential privacy. In this model we have multiple concurrent shufflers permuting messages from different, possibly overlapping, batches of users. Similarly to the standard (single) shuffle model, the privacy requirement is that the concatenation of all shuffled messages should be differentially private. We study the private continual summation problem (a.k.a. the counter problem) and show that the concurrent shuffle model allows for significantly improved error compared to a standard (single) shuffle model. Specifically, we give a summation algor…
Differential privacy (DP) provides rigorous privacy guarantees on individual's data while also allowing for accurate statistics to be conducted on the overall, sensitive dataset. To design a private system, first private algorithms must be designed that can quantify the privacy loss of each outcome that is released. However, private algorithms that inject noise into the computation are not sufficient to ensure individuals' data is protected due to many noisy results ultimately concentrating to the true, non-privatized result. Hence there have been several works providing precise formulas for h…
Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward: Given the model posterior one would simply use this as the prior for the next task. However, exact posterior evaluation is intractable with many models, especially with Bayesian neural networks (BNNs). Instead, posterior approximations are often sought. Unfortunately, when posterior approximations are used, prior-focused approaches do not succeed in evaluations…
Continual Learning addresses the challenge of learning a number of different tasks sequentially. The goal of maintaining knowledge of earlier tasks without re-accessing them starkly conflicts with standard SGD training for artificial neural networks. An influential method to tackle this problem without storing old data are so-called regularisation approaches. They measure the importance of each parameter for solving a given task and subsequently protect important parameters from large changes. In the literature, three ways to measure parameter importance have been put forward and they have ins…
Unifying Detection and Adaptation in Task-Free Continual Learning
School of Control Science and Engineering, Shandong University（山东大学控制科学与工程学院）；The Hong Kong University of Science and Technology（香港科技大学）；Shandong University（山东大学）；Qilu Hospital of Shandong University（山东大学齐鲁医院）
Modern machine learning systems need to be able to cope with constantly arriving and changing data. Two main areas of research dealing with such scenarios are continual learning and data stream mining. Continual learning focuses on accumulating knowledge and avoiding forgetting, assuming information once learned should be stored. Data stream mining focuses on adaptation to concept drift and discarding outdated information, assuming that only the most recent data is relevant. While these two areas are mainly being developed in separation, they offer complementary views on the problem of learnin…
Department of Computer Sciences University of Wisconsin — Madison（计算机科学系威斯康星大学麦迪逊分校）；Department of Electrical and Computer Engineering University of Wisconsin — Madison（电气与计算机工程系威斯康星大学麦迪逊分校）
The Hong Kong University of Science and Technology（香港科技大学）
Differentially private (DP) stochastic convex optimization (SCO) is ubiquitous in trustworthy machine learning algorithm design. This paper studies the DP-SCO problem with streaming data sampled from a distribution and arrives sequentially. We also consider the continual release model where parameters related to private information are updated and released upon each new data, often known as the online algorithms. Despite that numerous algorithms have been developed to achieve the optimal excess risks in different $\ell_p$ norm geometries, yet none of the existing ones can be adapted to the str…
