H. Brendan McMahan

Natalia Ponomareva, Hussein Hazimeh, Alex Kurakin et al. · mit

ML models are ubiquitous in real world applications and are a constant focus of research. At the same time, the community has started to realize the importance of protecting the privacy of ML training data. Differential Privacy (DP) has become a gold standard for making formal statements about data anonymization. However, while some adoption of DP has happened in industry, attempts to apply DP to real world complex ML models are still few and far between. The adoption of DP is hindered by limited practical guidance of what DP protection entails, what privacy guarantees to aim for, and the difficulty of achieving good privacy-utility-computation trade-offs for ML models. Tricks for tuning and maximizing performance are scattered among papers or stored in the heads of practitioners. Furthermore, the literature seems to present conflicting evidence on how and whether to apply architectural adjustments and which components are "safe" to use with DP. This work is a self-contained guide that gives an in-depth overview of the field of DP ML and presents information about achieving the best possible DP ML model with rigorous privacy guarantees. Our target audience is both researchers and practitioners. Researchers interested in DP for ML will benefit from a clear overview of current advances and areas for improvement. We include theory-focused sections that highlight important topics such as privacy accounting and its assumptions, and convergence. For a practitioner, we provide a background in DP theory and a clear step-by-step guide for choosing an appropriate privacy definition and approach, implementing DP training, potentially updating the model architecture, and tuning hyperparameters. For both researchers and practitioners, consistently and fully reporting privacy guarantees is critical, and so we propose a set of specific best practices for stating guarantees.

Zachary Charles, Arun Ganesh, Ryan McKenna et al.

We investigate practical and scalable algorithms for training large language models (LLMs) with user-level differential privacy (DP) in order to provably safeguard all the examples contributed by each user. We study two variants of DP-SGD with: (1) example-level sampling (ELS) and per-example gradient clipping, and (2) user-level sampling (ULS) and per-user gradient clipping. We derive a novel user-level DP accountant that allows us to compute provably tight privacy guarantees for ELS. Using this, we show that while ELS can outperform ULS in specific settings, ULS generally yields better results when each user has a diverse collection of examples. We validate our findings through experiments in synthetic mean estimation and LLM fine-tuning tasks under fixed compute budgets. We find that ULS is significantly better in settings where either (1) strong privacy guarantees are required, or (2) the compute budget is large. Notably, our focus on LLM-compatible training algorithms allows us to scale to models with hundreds of millions of parameters and datasets with hundreds of thousands of users.

Krishnamurthy Dvijotham, H. Brendan McMahan, Krishna Pillutla et al.

In the task of differentially private (DP) continual counting, we receive a stream of increments and our goal is to output an approximate running total of these increments, without revealing too much about any specific increment. Despite its simplicity, differentially private continual counting has attracted significant attention both in theory and in practice. Existing algorithms for differentially private continual counting are either inefficient in terms of their space usage or add an excessive amount of noise, inducing suboptimal utility. The most practical DP continual counting algorithms add carefully correlated Gaussian noise to the values. The task of choosing the covariance for this noise can be expressed in terms of factoring the lower-triangular matrix of ones (which computes prefix sums). We present two approaches from this class (for different parameter regimes) that achieve near-optimal utility for DP continual counting and only require logarithmic or polylogarithmic space (and time). Our first approach is based on a space-efficient streaming matrix multiplication algorithm for a class of Toeplitz matrices. We show that to instantiate this algorithm for DP continual counting, it is sufficient to find a low-degree rational function that approximates the square root on a circle in the complex plane. We then apply and extend tools from approximation theory to achieve this. We also derive efficient closed-forms for the objective function for arbitrarily many steps, and show direct numerical optimization yields a highly practical solution to the problem. Our second approach combines our first approach with a recursive construction similar to the binary tree mechanism.

Krishna Pillutla, Jalaj Upadhyay, Christopher A. Choquette-Choo et al.

This monograph explores the design and analysis of correlated noise mechanisms for differential privacy (DP), focusing on their application to private training of AI and machine learning models via the core primitive of estimation of weighted prefix sums. While typical DP mechanisms inject independent noise into each step of a stochastic gradient (SGD) learning algorithm in order to protect the privacy of the training data, a growing body of recent research demonstrates that introducing (anti-)correlations in the noise can significantly improve privacy-utility trade-offs by carefully canceling out some of the noise added on earlier steps in subsequent steps. Such correlated noise mechanisms, known variously as matrix mechanisms, factorization mechanisms, and DP-Follow-the-Regularized-Leader (DP-FTRL) when applied to learning algorithms, have also been influential in practice, with industrial deployment at a global scale.

H. Brendan McMahan, Krishna Pillutla

Buffered Linear Toeplitz (BLT) matrices are a family of parameterized lower-triangular matrices that play an important role in streaming differential privacy with correlated noise. Our main result is a BLT inversion theorem: the inverse of a BLT matrix is itself a BLT matrix with different parameters. We also present an efficient and differentiable $O(d^3)$ algorithm to compute the parameters of the inverse BLT matrix, where $d$ is the degree of the original BLT (typically $d < 10$). Our characterization enables direct optimization of BLT parameters for privacy mechanisms through automatic differentiation.

H. Brendan McMahan, Galen Andrew, Ulfar Erlingsson et al.

In this work we address the practical challenges of training machine learning models on privacy-sensitive datasets by introducing a modular approach that minimizes changes to training algorithms, provides a variety of configuration strategies for the privacy mechanism, and then isolates and simplifies the critical logic that computes the final privacy guarantees. A key challenge is that training algorithms often require estimating many different quantities (vectors) from the same set of examples --- for example, gradients of different layers in a deep learning architecture, as well as metrics and batch normalization parameters. Each of these may have different properties like dimensionality, magnitude, and tolerance to noise. By extending previous work on the Moments Accountant for the subsampled Gaussian mechanism, we can provide privacy for such heterogeneous sets of vectors, while also structuring the approach to minimize software engineering challenges.