Optimal Rates for Robust Stochastic Convex Optimization

The sensitivity of machine learning algorithms to outliers, particularly in high-dimensional spaces, necessitates the development of robust methods. Within the framework of $\epsilon$-contamination model, where the adversary can inspect and replace up to $\epsilon$ fraction of the samples, a fundamental open question is determining the optimal rates for robust stochastic convex optimization (robust SCO), provided the samples under $\epsilon$-contamination. We develop novel algorithms that achieve minimax-optimal excess risk (up to logarithmic factors) under the $\epsilon$-contamination model. Our approach advances beyonds existing algorithms, which are not only suboptimal but also constrained by stringent requirements, including Lipschitzness and smoothness conditions on sample functions.Our algorithms achieve optimal rates while removing these restrictive assumptions, and notably, remain effective for nonsmooth but Lipschitz population risks.

A Stochastic Optimization Framework for Private and Fair Learning From Decentralized Data

Machine learning models are often trained on sensitive data (e.g., medical records and race/gender) that is distributed across different "silos" (e.g., hospitals). These federated learning models may then be used to make consequential decisions, such as allocating healthcare resources. Two key challenges emerge in this setting: (i) maintaining the privacy of each person's data, even if other silos or an adversary with access to the central server tries to infer this data; (ii) ensuring that decisions are fair to different demographic groups (e.g., race/gender). In this paper, we develop a novel algorithm for private and fair federated learning (FL). Our algorithm satisfies inter-silo record-level differential privacy (ISRL-DP), a strong notion of private FL requiring that silo i's sent messages satisfy record-level differential privacy for all i. Our framework can be used to promote different fairness notions, including demographic parity and equalized odds. We prove that our algorithm converges under mild smoothness assumptions on the loss function, whereas prior work required strong convexity for convergence. As a byproduct of our analysis, we obtain the first convergence guarantee for ISRL-DP nonconvex-strongly concave min-max FL. Experiments demonstrate the state-of-the-art fairness-accuracy tradeoffs of our algorithm across different privacy levels.

Faster Algorithms for User-Level Private Stochastic Convex Optimization

We study private stochastic convex optimization (SCO) under user-level differential privacy (DP) constraints. In this setting, there are $n$ users (e.g., cell phones), each possessing $m$ data items (e.g., text messages), and we need to protect the privacy of each user's entire collection of data items. Existing algorithms for user-level DP SCO are impractical in many large-scale machine learning scenarios because: (i) they make restrictive assumptions on the smoothness parameter of the loss function and require the number of users to grow polynomially with the dimension of the parameter space; or (ii) they are prohibitively slow, requiring at least $(mn)^{3/2}$ gradient computations for smooth losses and $(mn)^3$ computations for non-smooth losses. To address these limitations, we provide novel user-level DP algorithms with state-of-the-art excess risk and runtime guarantees, without stringent assumptions. First, we develop a linear-time algorithm with state-of-the-art excess risk (for a non-trivial linear-time algorithm) under a mild smoothness assumption. Our second algorithm applies to arbitrary smooth losses and achieves optimal excess risk in $\approx (mn)^{9/8}$ gradient computations. Third, for non-smooth loss functions, we obtain optimal excess risk in $n^{11/8} m^{5/4}$ gradient computations. Moreover, our algorithms do not require the number of users to grow polynomially with the dimension.

Exploring User-level Gradient Inversion with a Diffusion Prior

We explore user-level gradient inversion as a new attack surface in distributed learning. We first investigate existing attacks on their ability to make inferences about private information beyond training data reconstruction. Motivated by the low reconstruction quality of existing methods, we propose a novel gradient inversion attack that applies a denoising diffusion model as a strong image prior in order to enhance recovery in the large batch setting. Unlike traditional attacks, which aim to reconstruct individual samples and suffer at large batch and image sizes, our approach instead aims to recover a representative image that captures the sensitive shared semantic information corresponding to the underlying user. Our experiments with face images demonstrate the ability of our methods to recover realistic facial images along with private user attributes.

Analyzing Inference Privacy Risks Through Gradients in Machine Learning

In distributed learning settings, models are iteratively updated with shared gradients computed from potentially sensitive user data. While previous work has studied various privacy risks of sharing gradients, our paper aims to provide a systematic approach to analyze private information leakage from gradients. We present a unified game-based framework that encompasses a broad range of attacks including attribute, property, distributional, and user disclosures. We investigate how different uncertainties of the adversary affect their inferential power via extensive experiments on five datasets across various data modalities. Our results demonstrate the inefficacy of solely relying on data aggregation to achieve privacy against inference attacks in distributed learning. We further evaluate five types of defenses, namely, gradient pruning, signed gradient descent, adversarial perturbations, variational information bottleneck, and differential privacy, under both static and adaptive adversary settings. We provide an information-theoretic view for analyzing the effectiveness of these defenses against inference from gradients. Finally, we introduce a method for auditing attribute inference privacy, improving the empirical estimation of worst-case privacy through crafting adversarial canary records.

Private Heterogeneous Federated Learning Without a Trusted Server Revisited: Error-Optimal and Communication-Efficient Algorithms for Convex Losses

We revisit the problem of federated learning (FL) with private data from people who do not trust the server or other silos/clients. In this context, every silo (e.g. hospital) has data from several people (e.g. patients) and needs to protect the privacy of each person's data (e.g. health records), even if the server and/or other silos try to uncover this data. Inter-Silo Record-Level Differential Privacy (ISRL-DP) prevents each silo's data from being leaked, by requiring that silo i's communications satisfy item-level differential privacy. Prior work arXiv:2203.06735 characterized the optimal excess risk bounds for ISRL-DP algorithms with homogeneous (i.i.d.) silo data and convex loss functions. However, two important questions were left open: (1) Can the same excess risk bounds be achieved with heterogeneous (non-i.i.d.) silo data? (2) Can the optimal risk bounds be achieved with fewer communication rounds? In this paper, we give positive answers to both questions. We provide novel ISRL-DP FL algorithms that achieve the optimal excess risk bounds in the presence of heterogeneous silo data. Moreover, our algorithms are more communication-efficient than the prior state-of-the-art. For smooth loss functions, our algorithm achieves the optimal excess risk bound and has communication complexity that matches the non-private lower bound. Additionally, our algorithms are more computationally efficient than the previous state-of-the-art.

Efficient Differentially Private Fine-Tuning of Diffusion Models

The recent developments of Diffusion Models (DMs) enable generation of astonishingly high-quality synthetic samples. Recent work showed that the synthetic samples generated by the diffusion model, which is pre-trained on public data and fully fine-tuned with differential privacy on private data, can train a downstream classifier, while achieving a good privacy-utility tradeoff. However, fully fine-tuning such large diffusion models with DP-SGD can be very resource-demanding in terms of memory usage and computation. In this work, we investigate Parameter-Efficient Fine-Tuning (PEFT) of diffusion models using Low-Dimensional Adaptation (LoDA) with Differential Privacy. We evaluate the proposed method with the MNIST and CIFAR-10 datasets and demonstrate that such efficient fine-tuning can also generate useful synthetic samples for training downstream classifiers, with guaranteed privacy protection of fine-tuning data. Our source code will be made available on GitHub.

How to Make the Gradients Small Privately: Improved Rates for Differentially Private Non-Convex Optimization

We provide a simple and flexible framework for designing differentially private algorithms to find approximate stationary points of non-convex loss functions. Our framework is based on using a private approximate risk minimizer to "warm start" another private algorithm for finding stationary points. We use this framework to obtain improved, and sometimes optimal, rates for several classes of non-convex loss functions. First, we obtain improved rates for finding stationary points of smooth non-convex empirical loss functions. Second, we specialize to quasar-convex functions, which generalize star-convex functions and arise in learning dynamical systems and training some neural nets. We achieve the optimal rate for this class. Third, we give an optimal algorithm for finding stationary points of functions satisfying the Kurdyka-Lojasiewicz (KL) condition. For example, over-parameterized neural networks often satisfy this condition. Fourth, we provide new state-of-the-art rates for stationary points of non-convex population loss functions. Fifth, we obtain improved rates for non-convex generalized linear models. A modification of our algorithm achieves nearly the same rates for second-order stationary points of functions with Lipschitz Hessian, improving over the previous state-of-the-art for each of the above problems.

Why Does Differential Privacy with Large Epsilon Defend Against Practical Membership Inference Attacks?

For small privacy parameter $\epsilon$, $\epsilon$-differential privacy (DP) provides a strong worst-case guarantee that no membership inference attack (MIA) can succeed at determining whether a person's data was used to train a machine learning model. The guarantee of DP is worst-case because: a) it holds even if the attacker already knows the records of all but one person in the data set; and b) it holds uniformly over all data sets. In practical applications, such a worst-case guarantee may be overkill: practical attackers may lack exact knowledge of (nearly all of) the private data, and our data set might be easier to defend, in some sense, than the worst-case data set. Such considerations have motivated the industrial deployment of DP models with large privacy parameter (e.g. $\epsilon \geq 7$), and it has been observed empirically that DP with large $\epsilon$ can successfully defend against state-of-the-art MIAs. Existing DP theory cannot explain these empirical findings: e.g., the theoretical privacy guarantees of $\epsilon \geq 7$ are essentially vacuous. In this paper, we aim to close this gap between theory and practice and understand why a large DP parameter can prevent practical MIAs. To tackle this problem, we propose a new privacy notion called practical membership privacy (PMP). PMP models a practical attacker's uncertainty about the contents of the private data. The PMP parameter has a natural interpretation in terms of the success rate of a practical MIA on a given data set. We quantitatively analyze the PMP parameter of two fundamental DP mechanisms: the exponential mechanism and Gaussian mechanism. Our analysis reveals that a large DP parameter often translates into a much smaller PMP parameter, which guarantees strong privacy against practical MIAs. Using our findings, we offer principled guidance for practitioners in choosing the DP parameter.

Optimal Differentially Private Learning with Public Data

Differential Privacy (DP) ensures that training a machine learning model does not leak private data. However, the cost of DP is lower model accuracy or higher sample complexity. In practice, we may have access to auxiliary public data that is free of privacy concerns. This has motivated the recent study of what role public data might play in improving the accuracy of DP models. In this work, we assume access to a given amount of public data and settle the following fundamental open questions: 1. What is the optimal (worst-case) error of a DP model trained over a private data set while having access to side public data? What algorithms are optimal? 2. How can we harness public data to improve DP model training in practice? We consider these questions in both the local and central models of DP. To answer the first question, we prove tight (up to constant factors) lower and upper bounds that characterize the optimal error rates of three fundamental problems: mean estimation, empirical risk minimization, and stochastic convex optimization. We prove that public data reduces the sample complexity of DP model training. Perhaps surprisingly, we show that the optimal error rates can be attained (up to constants) by either discarding private data and training a public model, or treating public data like it's private data and using an optimal DP algorithm. To address the second question, we develop novel algorithms which are "even more optimal" (i.e. better constants) than the asymptotically optimal approaches described above. For local DP mean estimation with public data, our algorithm is optimal including constants. Empirically, our algorithms show benefits over existing approaches for DP model training with side access to public data.