NeurIPS 2024 论文列表

To reduce the communication cost of differential privacy mechanisms, we introduce a novel construction, called Poisson private representation (PPR), designed to compress and simulate any local randomizer while ensuring local differential privacy. Unlike previous simulation-based local differential privacy mechanisms, PPR exactly preserves the joint distribution of the data and the output of the original local randomizer. Hence, the PPR-compressed privacy mechanism retains all desirable statistical properties of the original privacy mechanism such as unbiasedness and Gaussianity. Moreover, PPR achieves a compression size within a logarithmic gap from the theoretical lower bound. Using the PPR, we give a new order-wise trade-off between communication, accuracy, central and local differential privacy for distributed mean estimation. Experiment results on distributed mean estimation show that PPR consistently gives a better trade-off between communication, accuracy and central differential privacy compared to the coordinate subsampled Gaussian mechanism, while also providing local differential privacy.

We study distributed goodness-of-fit testing for discrete distribution under bandwidth and differential privacy constraints. Information constraint distributed goodness-of-fit testing is a problem that has received considerable attention recently. The important case of discrete distributions is theoretically well understood in the classical case where all data is available in one "central" location. In a federated setting, however, data is distributed across multiple "locations" (e.g. servers) and cannot readily be shared due to e.g. bandwidth or privacy constraints that each server needs to satisfy. We show how recently derived results for goodness-of-fit testing for the mean of a multivariate Gaussian model extend to the discrete distributions, by leveraging Le Cam's theory of statistical equivalence. In doing so, we derive matching minimax upper- and lower-bounds for the goodness-of-fit testing for discrete distributions under bandwidth or privacy constraints in the regime where number of samples held locally are large.

We study the interplay between local differential privacy (LDP) and robustness to Huber corruption and possibly heavy-tailed rewards in the context of multi-armed bandits (MABs). We consider two different practical settings: LDP-then-Corruption (LTC) where each user's locally private response might be further corrupted during the data collection process, and Corruption-then-LDP (CTL) where each user's raw data may be corrupted such that the LDP mechanism will only be applied to the corrupted data. To start with, we present the first tight characterization of the mean estimation error in high probability under both LTC and CTL settings. Leveraging this new result, we then present an almost tight characterization (up to log factor) of the minimax regret in online MABs and sub-optimality in offline MABs under both LTC and CTL settings, respectively. Our theoretical results in both settings are also corroborated by a set of systematic simulations. One key message in this paper is that LTC is a more difficult setting that leads to a worse performance guarantee compared to the CTL setting (in the minimax sense). Our sharp understanding of LTC and CTL also naturally allows us to give the first tight performance bounds for the most practical setting where corruption could happen both before and after the LDP mechanism. As an important by-product, we also give the first correct and tight regret bound for locally private and heavy-tailed online MABs, i.e., without Huber corruption, by identifying a fundamental flaw in the state-of-the-art.

Due to statistical lower bounds on the learnability of many function classes under privacy constraints, there has been recent interest in leveraging public data to improve the performance of private learning algorithms. In this model, algorithms must always guarantee differential privacy with respect to the private samples while also ensuring learning guarantees when the private data distribution is sufficiently close to that of the public data. Previous work has demonstrated that when sufficient public, unlabelled data is available, private learning can be made statistically tractable, but the resulting algorithms have all been computationally inefficient. In this work, we present the first computationally efficient, algorithms to provably leverage public data to learn privately whenever a function class is learnable non-privately, where our notion of computational efficiency is with respect to the number of calls to an optimization oracle for the function class. In addition to this general result, we provide specialized algorithms with improved sample complexities in the special cases when the function class is convex or when the task is binary classification.

Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating population densities in a geographic region, a small Wasserstein distance means that the estimate is able to capture roughly where the population mass is. In this work we study differentially private density estimation in the Wasserstein distance. We design and analyze instance-optimal algorithms for this problem that can adapt to easy instances. For distributions $P$ over $\mathbb{R}$, we consider a strong notion of instance-optimality: an algorithm that uniformly achieves the instance-optimal estimation rate is competitive with an algorithm that is told that the distribution is either $P$ or $Q_P$ for some distribution $Q_P$ whose probability density function (pdf) is within a factor of 2 of the pdf of $P$. For distributions over $\mathbb{R}^2$, we use a slightly different notion of instance optimality. We say that an algorithm is instance-optimal if it is competitive with an algorithm that is given a constant multiplicative approximation of the density of the distribution. We characterize the instance-optimal estimation rates in both these settings and show that they are uniformly achievable (up to polylogarithmic factors). Our approach for $\mathbb{R}^2$ extends to arbitrary metric spaces as it goes via hierarchically separated trees. As a special case our results lead to instance-optimal learning in TV distance for discrete distributions.

We propose reconstruction advantage measures to audit label privatization mechanisms. A reconstruction advantage measure quantifies the increase in an attacker's ability to infer the true label of an unlabeled example when provided with a private version of the labels in a dataset (e.g., aggregate of labels from different users or noisy labels output by randomized response), compared to an attacker that only observes the feature vectors, but may have prior knowledge of the correlation between features and labels. We consider two such auditing measures: one additive, and on multiplicative. These cover previous approaches taken in the literature on empirical auditing and differential privacy. These measures allow us to place a variety of proposed privatization schemes---some differentially private, some not---on the same footing. We analyze these measures theoretically under a distributional model which, we claim, encapsulates reasonable adversarial settings. We also quantify their behavior empirically on real and simulated prediction tasks. Across a range of experimental settings, we find that differentially private schemes dominate or match the privacy-utility tradeoff of more heuristic approaches.

In this work, we conduct a systematic study of stochastic saddle point problems (SSP) and stochastic variational inequalities (SVI) under the constraint of $(\epsilon,\delta)$-differential privacy (DP) in both Euclidean and non-Euclidean setups. We first consider Lipschitz convex-concave SSPs in the $\ell_p/\ell_q$ setup, $p,q\in[1,2]$. That is, we consider the case where the primal problem has an $\ell_p$-setup (i.e., the primal parameter is constrained to an $\ell_p$ bounded domain and the loss is $\ell_p$-Lipschitz with respect to the primal parameter) and the dual problem has an $\ell_q$ setup. Here, we obtain a bound of $\tilde{O}\big(\frac{1}{\sqrt{n}} + \frac{\sqrt{d}}{n\epsilon}\big)$ on the strong SP-gap, where $n$ is the number of samples and $d$ is the dimension. This rate is nearly optimal for any $p,q\in[1,2]$. Without additional assumptions, such as smoothness or linearity requirements, prior work under DP has only obtained this rate when $p=q=2$ (i.e., only in the Euclidean setup). Further, existing algorithms have each only been shown to work for specific settings of $p$ and $q$ and under certain assumptions on the loss and the feasible set, whereas we provide a general algorithm for DP SSPs whenever $p,q\in[1,2]$. Our result is obtained via a novel analysis of the recursive regularization algorithm. In particular, we develop new tools for analyzing generalization, which may be of independent interest. Next, we turn our attention towards SVIs with a monotone, bounded and Lipschitz operator and consider $\ell_p$-setups, $p\in[1,2]$. Here, we provide the first analysis which obtains a bound on the strong VI-gap of $\tilde{O}\big(\frac{1}{\sqrt{n}} + \frac{\sqrt{d}}{n\epsilon}\big)$. For $p-1=\Omega(1)$, this rate is near optimal due to existing lower bounds. To obtain this result, we develop a modified version of recursive regularization. Our analysis builds on the techniques we develop for SSPs as well as employing additional novel components which handle difficulties arising from adapting the recursive regularization framework to SVIs.

The modern study and use of surfaces is a research topic grounded in centuries of mathematical and empirical inquiry. From a mathematical point of view, curvature is an invariant that characterises the intrinsic geometry and the extrinsic shape of a surface. Yet, in modern applications the focus has shifted away from finding expressive representations of surfaces, and towards the design of efficient neural network architectures to process them. The literature suggests a tendency to either overlook the representation of the processed surface, or use overcomplicated representations whose ability to capture the essential features of a surface is opaque. We propose using curvature as the input of neural network architectures for surface processing, and explore this proposition through experiments making use of the shape operator. Our results show that using curvature as input leads to significant a increase in performance on segmentation and classification tasks, while allowing far less computational overhead than current methods.

Overparameterized stochastic differential equation (SDE) models have achieved remarkable success in various complex environments, such as PDE-constrained optimization, stochastic control and reinforcement learning, financial engineering, and neural SDEs. These models often feature system evolution coefficients that are parameterized by a high-dimensional vector $\theta \in \mathbb{R}^n$, aiming to optimize expectations of the SDE, such as a value function, through stochastic gradient ascent. Consequently, designing efficient gradient estimators for which the computational complexity scales well with $n$ is of significant interest. This paper introduces a novel unbiased stochastic gradient estimator—the generator gradient estimator—for which the computation time remains stable in $n$. In addition to establishing the validity of our methodology for general SDEs with jumps, we also perform numerical experiments that test our estimator in linear-quadratic control problems parameterized by high-dimensional neural networks. The results show a significant improvement in efficiency compared to the widely used pathwise differentiation method: Our estimator achieves near-constant computation times, increasingly outperforms its counterpart as $n$ increases, and does so without compromising estimation variance. These empirical findings highlight the potential of our proposed methodology for optimizing SDEs in contemporary applications.

We study the problem of learning mixtures of Gaussians with approximate differential privacy. We prove that roughly $kd^2 + k^{1.5} d^{1.75} + k^2 d$ samples suffice to learn a mixture of $k$ arbitrary $d$-dimensional Gaussians up to low total variation distance, with differential privacy. Our work improves over the previous best result (which required roughly $k^2 d^4$ samples) and is provably optimal when $d$ is much larger than $k^2$. Moreover, we give the first optimal bound for privately learning mixtures of $k$ univariate (i.e., $1$-dimensional) Gaussians. Importantly, we show that the sample complexity for learning mixtures of univariate Gaussians is linear in the number of components $k$, whereas the previous best sample complexity was quadratic in $k$. Our algorithms utilize various techniques, including the inverse sensitivity mechanism, sample compression for distributions, and methods for bounding volumes of sumsets.

We provide new lower bounds on the privacy guarantee of _multi-epoch_ Adaptive Batch Linear Queries (ABLQ) mechanism with _shuffled batch sampling_, demonstrating substantial gaps when compared to _Poisson subsampling_; prior analysis was limited to a single epoch. Since the privacy analysis of Differentially Private Stochastic Gradient Descent (DP-SGD) is obtained by analyzing the ABLQ mechanism, this brings into serious question the common practice of implementing Shuffling based DP-SGD, but reporting privacy parameters as if Poisson subsampling was used. To understand the impact of this gap on the utility of trained machine learning models, we introduce a novel practical approach to implement Poisson subsampling _at scale_ using massively parallel computation, and efficiently train models with the same. We provide a comparison between the utility of models trained with Poisson subsampling based DP-SGD, and the optimistic estimates of utility when using shuffling, via our new lower bounds on the privacy guarantee of ABLQ with shuffling.

We study convex resource allocation problems with $m$ hard constraints under $(\varepsilon,\delta)$-joint differential privacy (Joint-DP or JDP) in an offline setting. To approximately solve the problem, we propose a generic algorithm called Noisy Dual Mirror Descent. The algorithm applies noisy Mirror Descent to a dual problem from relaxing the hard constraints for private shadow prices, and then uses the shadow prices to coordinate allocations in the primal problem. Leveraging weak duality theory, we show that the optimality gap is upper bounded by $\mathcal{O}(\frac{\sqrt{m\ln(1/\delta)}}{\varepsilon})$, and constraint violation is no more than $\mathcal{O}(\frac{\sqrt{m\ln(1/\delta)}}{\varepsilon})$ per constraint. When strong duality holds, both preceding results can be improved to $\widetilde{\mathcal{O}}(\frac{\sqrt{\ln(1/\delta)}}{\varepsilon})$ by better utilizing the geometric structure of the dual space, which is neglected by existing works. To complement our results under strong duality, we derive a minimax lower bound $\Omega(\frac{m}{\varepsilon})$ for any JDP algorithm outputting feasible allocations. The lower bound matches our upper bounds up to some logarithmic factors for $\varepsilon\geq \max(1, 1/(n\gamma))$, where $n\gamma$ is the available resource level. Numerical studies further confirm the effectiveness of our algorithm.

We present PANORAMIA, a privacy leakage measurement framework for machine learning models that relies on membership inference attacks using generated data as non-members. By relying on generated non-member data, PANORAMIA eliminates the common dependency of privacy measurement tools on in-distribution non-member data. As a result, PANORAMIA does not modify the model, training data, or training process, and only requires access to a subset of the training data. We evaluate PANORAMIA on ML models for image and tabular data classification, as well as on large-scale language models.

We give the first polynomial-time, differentially node-private, and robust algorithm for estimating the edge density of Erdős-Rényi random graphs and their generalization, inhomogeneous random graphs. We further prove information-theoretical lower bounds, showing that the error rate of our algorithm is optimal up to logarithmic factors. Previous algorithms incur either exponential running time or suboptimal error rates. Two key ingredients of our algorithm are (1) a new sum-of-squares algorithm for robust edge density estimation, and (2) the reduction from privacy to robustness based on sum-of-squares exponential mechanisms due to Hopkins et al. (STOC 2023).

Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of _individual_ gradients. We start with new near-optimal bounds for the classic mean estimation problem but with sparse data, improving upon existing algorithms particularly for the high-dimensional regime. The corresponding lower bounds are based on a novel block-diagonal construction that is combined with existing DP mean estimation lower bounds. Next, we obtain pure- and approximate-DP algorithms with almost optimal rates for stochastic convex optimization with sparse gradients; the former represents the first nearly dimension-independent rates for this problem. Furthermore, by introducing novel analyses of bias reduction in mean estimation and randomly-stopped biased SGD we obtain nearly dimension-independent rates for near-stationary points for the empirical risk in nonconvex settings under approximate-DP.

We provide a new algorithmic framework for differentially private estimation of general functions that adapts to the hardness of the underlying dataset. We build upon previous work that gives a paradigm for selecting an output through the exponential mechanism based upon closeness of the inverse to the underlying dataset, termed the inverse sensitivity mechanism. Our framework will slightly modify the closeness metric and instead give a simple and efficient application of the sparse vector technique. While the inverse sensitivity mechanism was shown to be instance optimal, it was only with respect to a class of unbiased mechanisms such that the most likely outcome matches the underlying data. We break this assumption in order to more naturally navigate the bias-variance tradeoff, which will also critically allow for extending our method to unbounded data. In consideration of this tradeoff, we provide theoretical guarantees and empirical validation that our technique will be particularly effective when the distances to the underlying dataset are asymmetric. This asymmetry is inherent to a range of important problems including fundamental statistics such as variance, as well as commonly used machine learning performance metrics for both classification and regression tasks. We efficiently instantiate our method in $O(n)$ time for these problems and empirically show that our techniques will give substantially improved differentially private estimations.

As one of the most fundamental non-convex learning problems, ReLU regression under differential privacy (DP) constraints, especially in high-dimensional settings, remains a challenging area in privacy-preserving machine learning. Existing results are limited to the assumptions of bounded norm $ \|\mathbf{x}\|_2 \leq 1$, which becomes meaningless with increasing data dimensionality. In this work, we revisit the problem of DP ReLU regression in high-dimensional regimes. We propose two innovative algorithms DP-GLMtron and DP-TAGLMtron that outperform the conventional DPSGD. DP-GLMtron is based on a generalized linear model perceptron approach, integrating adaptive clipping and Gaussian mechanism for enhanced privacy. To overcome the constraints of small privacy budgets in DP-GLMtron, represented by $\widetilde{O}(\sqrt{1/N})$ where $N$ is the sample size, we introduce DP-TAGLMtron, which utilizes a tree aggregation protocol to balance privacy and utility effectively, showing that DP-TAGLMtron achieves comparable performance with only an additional factor of $O(\log N)$ in the utility upper bound. Moreover, our theoretical analysis extends beyond Gaussian-like data distributions to settings with eigenvalue decay, showing how data distribution impacts learning in high dimensions. Notably, our findings suggest that the utility upper bound could be independent of the dimension $d$, even when $d \gg N$. Experiments on synthetic and real-world datasets also validate our results.

Training generative models with differential privacy (DP) typically involves injecting noise into gradient updates or adapting the discriminator's training procedure. As a result, such approaches often struggle with hyper-parameter tuning and convergence. We consider the \emph{slicing privacy mechanism} that injects noise into random low-dimensional projections of the private data, and provide strong privacy guarantees for it. These noisy projections are used for training generative models. To enable optimizing generative models using this DP approach, we introduce the \emph{smoothed-sliced $f$-divergence} and show it enjoys statistical consistency. Moreover, we present a kernel-based estimator for this divergence, circumventing the need for adversarial training. Extensive numerical experiments demonstrate that our approach can generate synthetic data of higher quality compared with baselines. Beyond performance improvement, our method, by sidestepping the need for noisy gradients, offers data scientists the flexibility to adjust generator architecture and hyper-parameters, run the optimization over any number of epochs, and even restart the optimization process---all without incurring additional privacy costs.

Machine unlearning has raised significant interest with the adoption of laws ensuring the ``right to be forgotten''. Researchers have provided a probabilistic notion of approximate unlearning under a similar definition of Differential Privacy (DP), where privacy is defined as statistical indistinguishability to retraining from scratch. We propose Langevin unlearning, an unlearning framework based on noisy gradient descent with privacy guarantees for approximate unlearning problems. Langevin unlearning unifies the DP learning process and the privacy-certified unlearning process with many algorithmic benefits. These include approximate certified unlearning for non-convex problems, complexity saving compared to retraining, sequential and batch unlearning for multiple unlearning requests.