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The Price of Differential Privacy under Continual Observation

Palak Jain, Sofya Raskhodnikova, Satchit Sivakumar, Adam Smith

We study the accuracy of differentially private mechanisms in the continual release model. A continual release mechanism receives a sensitive dataset as a stream of $T$ inputs and produces, after receiving each input, an output that is accurate for all the inputs received so far. We provide the first strong lower bounds on the error of continual release mechanisms. In particular, for two fundamental problems that are closely related to empirical risk minimization and widely studied and used in the standard (batch) model, we prove that the worst case error of every continual release algorithm is $\tilde \Omega(T^{1/3})$ times larger than that of the best batch algorithm. Previous work shows only a $\Omega(\log T)$ gap between the worst case error achievable in these two models. We also formulate a model that allows for adaptively selected inputs, thus capturing dependencies that arise in many applications of continual release. Even though, in general, both privacy and accuracy are harder to attain in this model, we show that our lower bounds are matched by the error of simple algorithms that work even for adaptively selected inputs.

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MultiRobustBench: Benchmarking Robustness Against Multiple Attacks

Sihui Dai, Saeed Mahloujifar, Chong Xiang, Vikash Sehwag, Pin-Yu Chen, Prateek Mittal

The bulk of existing research in defending against adversarial examples focuses on defending against a single (typically bounded $\ell_p$-norm) attack, but for a practical setting, machine learning (ML) models should be robust to a wide variety of attacks. In this paper, we present the first unified framework for considering multiple attacks against ML models. Our framework is able to model different levels of learner's knowledge about the test-time adversary, allowing us to model robustness against unforeseen attacks and robustness against unions of attacks. Using our framework, we present the first leaderboard, MultiRobustBench (https://multirobustbench.github.io), for benchmarking multiattack evaluation which captures performance across attack types and attack strengths. We evaluate the performance of 16 defended models for robustness against a set of 9 different attack types, including $\ell_p$-based threat models, spatial transformations, and color changes, at 20 different attack strengths (180 attacks total). Additionally, we analyze the state of current defenses against multiple attacks. Our analysis shows that while existing defenses have made progress in terms of average robustness across the set of attacks used, robustness against the worst-case attack is still a big open problem as all existing models perform worse than random guessing.

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Effectively Using Public Data in Privacy Preserving Machine Learning

Milad Nasr, Saeed Mahloujifar, Xinyu Tang, Prateek Mittal, Amir Houmansadr

Differentially private (DP) machine learning techniques are notorious for their degradation of model utility (e.g., they degrade classification accuracy). A recent line of work has demonstrated that leveraging *public data* can improve the trade-off between privacy and utility when training models with DP guaranteed. In this work, we further explore the potential of using public data in DP models, showing that utility gains can in fact be significantly higher than what shown in prior works. Specifically, we introduce DOPE-SGD, a modified DP-SGD algorithm that leverages public data during its training. DOPE-SGD uses public data in two complementary ways: (1) it uses advance augmentation techniques that leverages public data to generate synthetic data that is effectively embedded in multiple steps of the training pipeline; (2) it uses a modified gradient clipping mechanism (which is a standard technique in DP training) to change the *origin* of gradient vectors using the information inferred from available public and synthetic data, therefore boosting utility. We also introduce a technique to ensemble intermediate DP models by leveraging the post processing property of differential privacy to further improve the accuracy of the predictions. Our experimental results demonstrate the effectiveness of our approach in improving the state-of-the-art in DP machine learning across multiple datasets, network architectures, and application domains. For instance, assuming access to $2,000$ public images, and for a privacy budget of $\varepsilon=2,\delta=10^{-5}$, our technique achieves an accuracy of $75.1\%$ on CIFAR10, significantly higher than $68.1\%$ achieved by the state of the art.

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Exploring the Limits of Model-Targeted Indiscriminate Data Poisoning Attacks

Yiwei Lu, Gautam Kamath, Yaoliang Yu

Indiscriminate data poisoning attacks aim to decrease a model's test accuracy by injecting a small amount of corrupted training data. Despite significant interest, existing attacks remain relatively ineffective against modern machine learning (ML) architectures. In this work, we introduce the notion of model poisoning reachability as a technical tool to explore the intrinsic limits of data poisoning attacks towards target parameters (i.e., model-targeted attacks). We derive an easily computable threshold to establish and quantify a surprising phase transition phenomenon among popular ML models: data poisoning attacks can achieve certain target parameters only when the poisoning ratio exceeds our threshold. Building on existing parameter corruption attacks and refining the Gradient Canceling attack, we perform extensive experiments to confirm our theoretical findings, test the predictability of our transition threshold, and significantly improve existing indiscriminate data poisoning baselines over a range of datasets and models. Our work highlights the critical role played by the poisoning ratio, and sheds new insights on existing empirical results, attacks and mitigation strategies in data poisoning.

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Concurrent Shuffle Differential Privacy Under Continual Observation

Jay Tenenbaum, Haim Kaplan, Yishay Mansour, Uri Stemmer

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) shuffler 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) shuffler model. Specifically, we give a summation algorithm with error $\tilde{O}(n^{1/(2k+1)})$ with $k$ concurrent shufflers on a sequence of length $n$. Furthermore, we prove that this bound is tight for any $k$, even if the algorithm can choose the sizes of the batches adaptively. For $k=\log n$ shufflers, the resulting error is polylogarithmic, much better than $\tilde{\Theta}(n^{1/3})$ which we show is the smallest possible with a single shuffler. We use our online summation algorithm to get algorithms with improved regret bounds for the contextual linear bandit problem. In particular we get optimal $\tilde{O}(\sqrt{n})$ regret with $k= \tilde{\Omega}(\log n)$ concurrent shufflers.

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Fully-Adaptive Composition in Differential Privacy

Justin Whitehouse, Aaditya Ramdas, Ryan Rogers, Steven Wu

Composition is a key feature of differential privacy. Well-known advanced composition theorems allow one to query a private database quadratically more times than basic privacy composition would permit. However, these results require that the privacy parameters of all algorithms be fixed before interacting with the data. To address this, Rogers et al. introduced fully adaptive composition, wherein both algorithms and their privacy parameters can be selected adaptively. They defined two probabilistic objects to measure privacy in adaptive composition: privacy filters, which provide differential privacy guarantees for composed interactions, and privacy odometers, time-uniform bounds on privacy loss. There are substantial gaps between advanced composition and existing filters and odometers. First, existing filters place stronger assumptions on the algorithms being composed. Second, these odometers and filters suffer from large constants, making them impractical. We construct filters that match the rates of advanced composition, including constants, despite allowing for adaptively chosen privacy parameters. En route we also derive a privacy filter for approximate zCDP. We also construct several general families of odometers. These odometers match the tightness of advanced composition at an arbitrary, preselected point in time, or at all points in time simultaneously, up to a doubly-logarithmic factor. We obtain our results by leveraging advances in martingale concentration. In sum, we show that fully adaptive privacy is obtainable at almost no loss.

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HETAL: Efficient Privacy-preserving Transfer Learning with Homomorphic Encryption

Seewoo Lee, Garam Lee, Jung Woo Kim, Junbum Shin, Mun-Kyu Lee

Transfer learning is a de facto standard method for efficiently training machine learning models for data-scarce problems by adding and fine-tuning new classification layers to a model pre-trained on large datasets. Although numerous previous studies proposed to use homomorphic encryption to resolve the data privacy issue in transfer learning in the machine learning as a service setting, most of them only focused on encrypted inference. In this study, we present HETAL, an efficient Homomorphic Encryption based Transfer Learning algorithm, that protects the client's privacy in training tasks by encrypting the client data using the CKKS homomorphic encryption scheme. HETAL is the first practical scheme that strictly provides encrypted training, adopting validation-based early stopping and achieving the accuracy of nonencrypted training. We propose an efficient encrypted matrix multiplication algorithm, which is 1.8 to 323 times faster than prior methods, and a highly precise softmax approximation algorithm with increased coverage. The experimental results for five well-known benchmark datasets show total training times of 567--3442 seconds, which is less than an hour.

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Understanding Backdoor Attacks through the Adaptability Hypothesis

Xun Xian, Ganghua Wang, Jayanth Srinivasa, Ashish Kundu, Xuan Bi, Mingyi Hong, Jie Ding

A poisoning backdoor attack is a rising security concern for deep learning. This type of attack can result in the backdoored model functioning normally most of the time but exhibiting abnormal behavior when presented with inputs containing the backdoor trigger, making it difficult to detect and prevent. In this work, we propose the adaptability hypothesis to understand when and why a backdoor attack works for general learning models, including deep neural networks, based on the theoretical investigation of classical kernel-based learning models. The adaptability hypothesis postulates that for an effective attack, the effect of incorporating a new dataset on the predictions of the original data points will be small, provided that the original data points are distant from the new dataset. Experiments on benchmark image datasets and state-of-the-art backdoor attacks for deep neural networks are conducted to corroborate the hypothesis. Our finding provides insight into the factors that affect the attack's effectiveness and has implications for the design of future attacks and defenses.

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GuardHFL: Privacy Guardian for Heterogeneous Federated Learning

Hanxiao Chen, Meng Hao, Hongwei Li, Kangjie Chen, Guowen Xu, Tianwei Zhang, Xilin Zhang

Heterogeneous federated learning (HFL) enables clients with different computation and communication capabilities to collaboratively train their own customized models via a query-response paradigm on auxiliary datasets. However, such a paradigm raises serious privacy concerns due to the leakage of highly sensitive query samples and response predictions. We put forth GuardHFL, the first-of-its-kind efficient and privacy-preserving HFL framework. GuardHFL is equipped with a novel HFL-friendly secure querying scheme built on lightweight secret sharing and symmetric-key techniques. The core of GuardHFL is two customized multiplication and comparison protocols, which substantially boost the execution efficiency. Extensive evaluations demonstrate that GuardHFL significantly outperforms the alternative instantiations based on existing state-of-the-art techniques in both runtime and communication cost.

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Preprocessors Matter! Realistic Decision-Based Attacks on Machine Learning Systems

Chawin Sitawarin, Florian Tramèr, Nicholas Carlini

Decision-based attacks construct adversarial examples against a machine learning (ML) model by making only hard-label queries. These attacks have mainly been applied directly to standalone neural networks. However, in practice, ML models are just one component of a larger learning system. We find that by adding a single preprocessor in front of a classifier, state-of-the-art query-based attacks are up to seven× less effective at attacking a prediction pipeline than at attacking the model alone. We explain this discrepancy by the fact that most preprocessors introduce some notion of invariance to the input space. Hence, attacks that are unaware of this invariance inevitably waste a large number of queries to re-discover or overcome it. We, therefore, develop techniques to (i) reverse-engineer the preprocessor and then (ii) use this extracted information to attack the end-to-end system. Our preprocessors extraction method requires only a few hundred queries, and our preprocessor-aware attacks recover the same efficacy as when attacking the model alone. The code can be found at https://github.com/google-research/preprocessor-aware-black-box-attack.

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Adversarial Parameter Attack on Deep Neural Networks

Lijia Yu, Yihan Wang, Xiao-Shan Gao

The parameter perturbation attack is a safety threat to deep learning, where small parameter perturbations are made such that the attacked network gives wrong or desired labels of the adversary to specified inputs. However, such attacks could be detected by the user, because the accuracy of the attacked network will reduce and the network cannot work normally. To make the attack more stealthy, in this paper, the adversarial parameter attack is proposed, in which small perturbations to the parameters of the network are made such that the accuracy of the attacked network does not decrease much, but its robustness against adversarial example attacks becomes much lower. As a consequence, the attacked network performs normally on standard samples, but is much more vulnerable to adversarial attacks. The existence of nearly perfect adversarial parameters under $L_\infty$ norm and $L_0$ norm is proved under reasonable conditions. Algorithms are given which can be used to produce high quality adversarial parameters for the commonly used networks trained with various robust training methods, in that the robustness of the attacked networks decreases significantly when they are evaluated using various adversarial attack methods.

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Sketching Meets Differential Privacy: Fast Algorithm for Dynamic Kronecker Projection Maintenance

Zhao Song, Xin Yang, Yuanyuan Yang, Lichen Zhang

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix ${\sf A}$ and a positive semi-definite matrix $W\in \mathbb{R}^{n\times n}$ with a sparse eigenbasis, we consider the task of maintaining the projection in the form of ${\sf B}^\top({\sf B}{\sf B}^\top)^{-1}{\sf B}$, where ${\sf B}={\sf A}(W\otimes I)$ or ${\sf B}={\sf A}(W^{1/2}\otimes W^{1/2})$. At each iteration, the weight matrix $W$ receives a low rank change and we receive a new vector $h$. The goal is to maintain the projection matrix and answer the query ${\sf B}^\top({\sf B}{\sf B}^\top)^{-1}{\sf B}h$ with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

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Federated Linear Contextual Bandits with User-level Differential Privacy

Ruiquan Huang, Huanyu Zhang, Luca Melis, Milan Shen, Meisam Hejazinia, Jing Yang

This paper studies federated linear contextual bandits under the notion of user-level differential privacy (DP). We first introduce a unified federated bandits framework that can accommodate various definitions of DP in the sequential decision-making setting. We then formally introduce user-level central DP (CDP) and local DP (LDP) in the federated bandits framework, and investigate the fundamental trade-offs between the learning regrets and the corresponding DP guarantees in a federated linear contextual bandits model. For CDP, we propose a federated algorithm termed as $\texttt{ROBIN}$ and show that it is near-optimal in terms of the number of clients $M$ and the privacy budget $\varepsilon$ by deriving nearly-matching upper and lower regret bounds when user-level DP is satisfied. For LDP, we obtain several lower bounds, indicating that learning under user-level $(\varepsilon,\delta)$-LDP must suffer a regret blow-up factor at least $\min\{1/\varepsilon,M\}$ or $\min\{1/\sqrt{\varepsilon},\sqrt{M}\}$ under different conditions.

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Are Diffusion Models Vulnerable to Membership Inference Attacks?

Jinhao Duan, Fei Kong, Shiqi Wang, Xiaoshuang Shi, Kaidi Xu

Diffusion-based generative models have shown great potential for image synthesis, but there is a lack of research on the security and privacy risks they may pose. In this paper, we investigate the vulnerability of diffusion models to Membership Inference Attacks (MIAs), a common privacy concern. Our results indicate that existing MIAs designed for GANs or VAE are largely ineffective on diffusion models, either due to inapplicable scenarios (e.g., requiring the discriminator of GANs) or inappropriate assumptions (e.g., closer distances between synthetic samples and member samples). To address this gap, we propose Step-wise Error Comparing Membership Inference (SecMI), a query-based MIA that infers memberships by assessing the matching of forward process posterior estimation at each timestep. SecMI follows the common overfitting assumption in MIA where member samples normally have smaller estimation errors, compared with hold-out samples. We consider both the standard diffusion models, e.g., DDPM, and the text-to-image diffusion models, e.g., Latent Diffusion Models and Stable Diffusion. Experimental results demonstrate that our methods precisely infer the membership with high confidence on both of the two scenarios across multiple different datasets. Code is available at https://github.com/jinhaoduan/SecMI.

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Differential Privacy has Bounded Impact on Fairness in Classification

Paul Mangold, Michaël Perrot, Aurélien Bellet, Marc Tommasi

We theoretically study the impact of differential privacy on fairness in classification. We prove that, given a class of models, popular group fairness measures are pointwise Lipschitz-continuous with respect to the parameters of the model. This result is a consequence of a more general statement on accuracy conditioned on an arbitrary event (such as membership to a sensitive group), which may be of independent interest. We use this Lipschitz property to prove a non-asymptotic bound showing that, as the number of samples increases, the fairness level of private models gets closer to the one of their non-private counterparts. This bound also highlights the importance of the confidence margin of a model on the disparate impact of differential privacy.

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Run-off Election: Improved Provable Defense against Data Poisoning Attacks

Keivan Rezaei, Kiarash Banihashem, Atoosa Chegini, Soheil Feizi

In data poisoning attacks, an adversary tries to change a model's prediction by adding, modifying, or removing samples in the training data. Recently, *ensemble-based* approaches for obtaining *provable* defenses against data poisoning have been proposed where predictions are done by taking a majority vote across multiple base models. In this work, we show that merely considering the majority vote in ensemble defenses is wasteful as it does not effectively utilize available information in the logits layers of the base models. Instead, we propose *Run-Off Election (ROE)*, a novel aggregation method based on a two-round election across the base models: In the first round, models vote for their preferred class and then a second, *Run-Off* election is held between the top two classes in the first round. Based on this approach, we propose DPA+ROE and FA+ROE defense methods based on Deep Partition Aggregation (DPA) and Finite Aggregation (FA) approaches from prior work. We evaluate our methods on MNIST, CIFAR-10, and GTSRB and obtain improvements in certified accuracy by up to $3\%$-$4\%$. Also, by applying ROE on a boosted version of DPA, we gain improvements around $12\%$-$27\%$ comparing to the current state-of-the-art, establishing **a new state-of-the-art** in (pointwise) certified robustness against data poisoning. In many cases, our approach outperforms the state-of-the-art, even when using 32 times less computational power.

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Rethinking Backdoor Attacks

Alaa Khaddaj, Guillaume Leclerc, Aleksandar Makelov, Kristian Georgiev, Hadi Salman, Andrew Ilyas, Aleksander Madry

In a *backdoor attack*, an adversary inserts maliciously constructed backdoor examples into a training set to make the resulting model vulnerable to manipulation. Defending against such attacks involves viewing inserted examples as outliers in the training set and using techniques from robust statistics to detect and remove them. In this work, we present a different approach to the backdoor attack problem. Specifically, we show that without structural information about the training data distribution, backdoor attacks are *indistinguishable* from naturally-occuring features in the data---and thus impossible to "detect" in a general sense. Then, guided by this observation, we revisit existing defenses against backdoor attacks and characterize the (often latent) assumptions they make, and on which they depend. Finally, we explore an alternative perspective on backdoor attacks: one that assumes these attacks correspond to the *strongest* feature in the training data. Under this assumption (which we make formal) we develop a new primitive for detecting backdoor attacks. Our primitive naturally gives rise to a detection algorithm that comes with theoretical guarantees, and is effective in practice.

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Differential Privacy, Linguistic Fairness, and Training Data Influence: Impossibility and Possibility Theorems for Multilingual Language Models

Phillip Rust, Anders Søgaard

Language models such as mBERT, XLM-R, and BLOOM aim to achieve multilingual generalization or compression to facilitate transfer to a large number of (potentially unseen) languages. However, these models should ideally also be private, linguistically fair, and transparent, by relating their predictions to training data. Can these requirements be simultaneously satisfied? We show that multilingual compression and linguistic fairness are compatible with differential privacy, but that differential privacy is at odds with training data influence sparsity, an objective for transparency. We further present a series of experiments on two common NLP tasks and evaluate multilingual compression and training data influence sparsity under different privacy guarantees, exploring these trade-offs in more detail. Our results suggest that we need to develop ways to jointly optimize for these objectives in order to find practical trade-offs.

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Bayesian Estimation of Differential Privacy

Santiago Zanella-Beguelin, Lukas Wutschitz, Shruti Tople, Ahmed Salem, Victor Rühle, Andrew Paverd, Mohammad Naseri, Boris Köpf, Daniel Jones

Algorithms such as Differentially Private SGD enable training machine learning models with formal privacy guarantees. However, because these guarantees hold with respect to unrealistic adversaries, the protection afforded against practical attacks is typically much better. An emerging strand of work empirically estimates the protection afforded by differentially private training as a confidence interval for the privacy budget $\hat{\varepsilon}$ spent with respect to specific threat models. Existing approaches derive confidence intervals for $\hat{\varepsilon}$ from confidence intervals for false positive and false negative rates of membership inference attacks, which requires training an impractically large number of models to get intervals that can be acted upon. We propose a novel, more efficient Bayesian approach that brings privacy estimates within the reach of practitioners. Our approach reduces sample size by computing a posterior for $\hat{\varepsilon}$ (not just a confidence interval) from the joint posterior of the false positive and false negative rates of membership inference attacks. We implement an end-to-end system for privacy estimation that integrates our approach and state-of-the-art membership inference attacks, and evaluate it on text and vision classification tasks. For the same number of samples, we see a reduction in interval width of up to 40% compared to prior work.

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Privacy-Aware Compression for Federated Learning Through Numerical Mechanism Design

Chuan Guo, Kamalika Chaudhuri, Pierre Stock, Michael Rabbat

In private federated learning (FL), a server aggregates differentially private updates from a large number of clients in order to train a machine learning model. The main challenge in this setting is balancing privacy with both classification accuracy of the learnt model as well as the number of bits communicated between the clients and server. Prior work has achieved a good trade-off by designing a privacy-aware compression mechanism, called the minimum variance unbiased (MVU) mechanism, that numerically solves an optimization problem to determine the parameters of the mechanism. This paper builds upon it by introducing a new interpolation procedure in the numerical design process that allows for a far more efficient privacy analysis. The result is the new Interpolated MVU mechanism that is more scalable, has a better privacy-utility trade-off, and provides SOTA results on communication-efficient private FL on a variety of datasets.

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