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Thomas Steinke

Publications and source records attributed to Thomas Steinke.

At least 37 records · Page 2Linked to original sources
arXiv2023

Faster Differentially Private Convex Optimization via Second-Order Methods

Differentially private (stochastic) gradient descent is the workhorse of DP private machine learning in both the convex and non-convex settings. Without privacy constraints, second-order methods, like Newton's method, converge faster than first-order methods like gradient descent. In this work, we investigate the prospect of using the second-order information from the loss function to accelerate DP convex optimization. We first develop a private variant of the regularized cubic Newton method of Nesterov and Polyak, and show that for the class of strongly convex loss functions, our algorithm has quadratic convergence and achieves the optimal excess loss. We then design a practical second-order DP algorithm for the unconstrained logistic regression problem. We theoretically and empirically study the performance of our algorithm. Empirical results show our algorithm consistently achieves the best excess loss compared to other baselines and is 10-40x faster than DP-GD/DP-SGD.

cs.LG↗
arXiv2023

Differentially Private Medians and Interior Points for Non-Pathological Data

We construct differentially private estimators with low sample complexity that estimate the median of an arbitrary distribution over $\mathbb{R}$ satisfying very mild moment conditions. Our result stands in contrast to the surprising negative result of Bun et al. (FOCS 2015) that showed there is no differentially private estimator with any finite sample complexity that returns any non-trivial approximation to the median of an arbitrary distribution.

cs.DS↗
arXiv2023

Privacy Auditing with One (1) Training Run

We propose a scheme for auditing differentially private machine learning systems with a single training run. This exploits the parallelism of being able to add or remove multiple training examples independently. We analyze this using the connection between differential privacy and statistical generalization, which avoids the cost of group privacy. Our auditing scheme requires minimal assumptions about the algorithm and can be applied in the black-box or white-box setting.

cs.LG↗
arXiv2023

Why Is Public Pretraining Necessary for Private Model Training?

In the privacy-utility tradeoff of a model trained on benchmark language and vision tasks, remarkable improvements have been widely reported with the use of pretraining on publicly available data. This is in part due to the benefits of transfer learning, which is the standard motivation for pretraining in non-private settings. However, the stark contrast in the improvement achieved through pretraining under privacy compared to non-private settings suggests that there may be a deeper, distinct cause driving these gains. To explain this phenomenon, we hypothesize that the non-convex loss landscape of a model training necessitates an optimization algorithm to go through two phases. In the first, the algorithm needs to select a good "basin" in the loss landscape. In the second, the algorithm solves an easy optimization within that basin. The former is a harder problem to solve with private data, while the latter is harder to solve with public data due to a distribution shift or data scarcity. Guided by this intuition, we provide theoretical constructions that provably demonstrate the separation between private training with and without public pretraining. Further, systematic experiments on CIFAR10 and LibriSpeech provide supporting evidence for our hypothesis.

cs.LG↗
arXiv2023

Tight Auditing of Differentially Private Machine Learning

Auditing mechanisms for differential privacy use probabilistic means to empirically estimate the privacy level of an algorithm. For private machine learning, existing auditing mechanisms are tight: the empirical privacy estimate (nearly) matches the algorithm's provable privacy guarantee. But these auditing techniques suffer from two limitations. First, they only give tight estimates under implausible worst-case assumptions (e.g., a fully adversarial dataset). Second, they require thousands or millions of training runs to produce non-trivial statistical estimates of the privacy leakage. This work addresses both issues. We design an improved auditing scheme that yields tight privacy estimates for natural (not adversarially crafted) datasets -- if the adversary can see all model updates during training. Prior auditing works rely on the same assumption, which is permitted under the standard differential privacy threat model. This threat model is also applicable, e.g., in federated learning settings. Moreover, our auditing scheme requires only two training runs (instead of thousands) to produce tight privacy estimates, by adapting recent advances in tight composition theorems for differential privacy. We demonstrate the utility of our improved auditing schemes by surfacing implementation bugs in private machine learning code that eluded prior auditing techniques.

cs.LG↗
arXiv2022

Composition of Differential Privacy & Privacy Amplification by Subsampling

This chapter is meant to be part of the book "Differential Privacy for Artificial Intelligence Applications." We give an introduction to the most important property of differential privacy -- composition: running multiple independent analyses on the data of a set of people will still be differentially private as long as each of the analyses is private on its own -- as well as the related topic of privacy amplification by subsampling. This chapter introduces the basic concepts and gives proofs of the key results needed to apply these tools in practice.

cs.CR↗
arXiv2022

The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation

We consider training models on private data that are distributed across user devices. To ensure privacy, we add on-device noise and use secure aggregation so that only the noisy sum is revealed to the server. We present a comprehensive end-to-end system, which appropriately discretizes the data and adds discrete Gaussian noise before performing secure aggregation. We provide a novel privacy analysis for sums of discrete Gaussians and carefully analyze the effects of data quantization and modular summation arithmetic. Our theoretical guarantees highlight the complex tension between communication, privacy, and accuracy. Our extensive experimental results demonstrate that our solution is essentially able to match the accuracy to central differential privacy with less than 16 bits of precision per value.

cs.LG↗
arXiv2022

Algorithms with More Granular Differential Privacy Guarantees

Differential privacy is often applied with a privacy parameter that is larger than the theory suggests is ideal; various informal justifications for tolerating large privacy parameters have been proposed. In this work, we consider partial differential privacy (DP), which allows quantifying the privacy guarantee on a per-attribute basis. In this framework, we study several basic data analysis and learning tasks, and design algorithms whose per-attribute privacy parameter is smaller that the best possible privacy parameter for the entire record of a person (i.e., all the attributes).

cs.CR↗
arXiv2022

Public Data-Assisted Mirror Descent for Private Model Training

In this paper, we revisit the problem of using in-distribution public data to improve the privacy/utility trade-offs for differentially private (DP) model training. (Here, public data refers to auxiliary data sets that have no privacy concerns.) We design a natural variant of DP mirror descent, where the DP gradients of the private/sensitive data act as the linear term, and the loss generated by the public data as the mirror map. We show that, for linear regression with feature vectors drawn from a non-isotropic sub-Gaussian distribution, our algorithm, PDA-DPMD (a variant of mirror descent), provides population risk guarantees that are asymptotically better than the best known guarantees under DP (without having access to public data), when the number of public data samples ($n_{\sf pub}$) is sufficiently large. We further show that our algorithm has natural "noise stability" properties that control the variance due to noise added to ensure DP. We demonstrate the efficacy of our algorithm by showing privacy/utility trade-offs on four benchmark datasets (StackOverflow, WikiText-2, CIFAR-10, and EMNIST). We show that our algorithm not only significantly improves over traditional DP-SGD, which does not have access to public data, but to our knowledge is the first to improve over DP-SGD on models that have been pre-trained with public data.

cs.LG↗
arXiv2022

Debugging Differential Privacy: A Case Study for Privacy Auditing

Differential Privacy can provide provable privacy guarantees for training data in machine learning. However, the presence of proofs does not preclude the presence of errors. Inspired by recent advances in auditing which have been used for estimating lower bounds on differentially private algorithms, here we show that auditing can also be used to find flaws in (purportedly) differentially private schemes. In this case study, we audit a recent open source implementation of a differentially private deep learning algorithm and find, with 99.99999999% confidence, that the implementation does not satisfy the claimed differential privacy guarantee.

cs.LG↗
arXiv2022

Hyperparameter Tuning with Renyi Differential Privacy

For many differentially private algorithms, such as the prominent noisy stochastic gradient descent (DP-SGD), the analysis needed to bound the privacy leakage of a single training run is well understood. However, few studies have reasoned about the privacy leakage resulting from the multiple training runs needed to fine tune the value of the training algorithm's hyperparameters. In this work, we first illustrate how simply setting hyperparameters based on non-private training runs can leak private information. Motivated by this observation, we then provide privacy guarantees for hyperparameter search procedures within the framework of Renyi Differential Privacy. Our results improve and extend the work of Liu and Talwar (STOC 2019). Our analysis supports our previous observation that tuning hyperparameters does indeed leak private information, but we prove that, under certain assumptions, this leakage is modest, as long as each candidate training run needed to select hyperparameters is itself differentially private.

cs.LG↗
arXiv2022

A Private and Computationally-Efficient Estimator for Unbounded Gaussians

We give the first polynomial-time, polynomial-sample, differentially private estimator for the mean and covariance of an arbitrary Gaussian distribution $\mathcal{N}(μ,Σ)$ in $\mathbb{R}^d$. All previous estimators are either nonconstructive, with unbounded running time, or require the user to specify a priori bounds on the parameters $μ$ and $Σ$. The primary new technical tool in our algorithm is a new differentially private preconditioner that takes samples from an arbitrary Gaussian $\mathcal{N}(0,Σ)$ and returns a matrix $A$ such that $A ΣA^T$ has constant condition number.

stat.ML↗
arXiv2021

Privately Learning Subspaces

Private data analysis suffers a costly curse of dimensionality. However, the data often has an underlying low-dimensional structure. For example, when optimizing via gradient descent, the gradients often lie in or near a low-dimensional subspace. If that low-dimensional structure can be identified, then we can avoid paying (in terms of privacy or accuracy) for the high ambient dimension. We present differentially private algorithms that take input data sampled from a low-dimensional linear subspace (possibly with a small amount of error) and output that subspace (or an approximation to it). These algorithms can serve as a pre-processing step for other procedures.

cs.CR↗
arXiv2021

PAC-Bayes, MAC-Bayes and Conditional Mutual Information: Fast rate bounds that handle general VC classes

We give a novel, unified derivation of conditional PAC-Bayesian and mutual information (MI) generalization bounds. We derive conditional MI bounds as an instance, with special choice of prior, of conditional MAC-Bayesian (Mean Approximately Correct) bounds, itself derived from conditional PAC-Bayesian bounds, where `conditional' means that one can use priors conditioned on a joint training and ghost sample. This allows us to get nontrivial PAC-Bayes and MI-style bounds for general VC classes, something recently shown to be impossible with standard PAC-Bayesian/MI bounds. Second, it allows us to get faster rates of order $O \left(({\text{KL}}/n)^γ\right)$ for $γ> 1/2$ if a Bernstein condition holds and for exp-concave losses (with $γ=1$), which is impossible with both standard PAC-Bayes generalization and MI bounds. Our work extends the recent work by Steinke and Zakynthinou [2020] who handle MI with VC but neither PAC-Bayes nor fast rates, the recent work of Hellström and Durisi [2020] who extend the latter to the PAC-Bayes setting via a unifying exponential inequality, and Mhammedi et al. [2019] who initiated fast rate PAC-Bayes generalization error bounds but handle neither MI nor general VC classes.

cs.LG↗
arXiv2021

Leveraging Public Data for Practical Private Query Release

In many statistical problems, incorporating priors can significantly improve performance. However, the use of prior knowledge in differentially private query release has remained underexplored, despite such priors commonly being available in the form of public datasets, such as previous US Census releases. With the goal of releasing statistics about a private dataset, we present PMW^Pub, which -- unlike existing baselines -- leverages public data drawn from a related distribution as prior information. We provide a theoretical analysis and an empirical evaluation on the American Community Survey (ACS) and ADULT datasets, which shows that our method outperforms state-of-the-art methods. Furthermore, PMW^Pub scales well to high-dimensional data domains, where running many existing methods would be computationally infeasible.

cs.LG↗
arXiv2021

Evading Curse of Dimensionality in Unconstrained Private GLMs via Private Gradient Descent

We revisit the well-studied problem of differentially private empirical risk minimization (ERM). We show that for unconstrained convex generalized linear models (GLMs), one can obtain an excess empirical risk of $\tilde O\left(\sqrt{\texttt{rank}}/εn\right)$, where ${\texttt{rank}}$ is the rank of the feature matrix in the GLM problem, $n$ is the number of data samples, and $ε$ is the privacy parameter. This bound is attained via differentially private gradient descent (DP-GD). Furthermore, via the first lower bound for unconstrained private ERM, we show that our upper bound is tight. In sharp contrast to the constrained ERM setting, there is no dependence on the dimensionality of the ambient model space ($p$). (Notice that ${\texttt{rank}}\leq \min\{n, p\}$.) Besides, we obtain an analogous excess population risk bound which depends on ${\texttt{rank}}$ instead of $p$. For the smooth non-convex GLM setting (i.e., where the objective function is non-convex but preserves the GLM structure), we further show that DP-GD attains a dimension-independent convergence of $\tilde O\left(\sqrt{\texttt{rank}}/εn\right)$ to a first-order-stationary-point of the underlying objective. Finally, we show that for convex GLMs, a variant of DP-GD commonly used in practice (which involves clipping the individual gradients) also exhibits the same dimension-independent convergence to the minimum of a well-defined objective. To that end, we provide a structural lemma that characterizes the effect of clipping on the optimization profile of DP-GD.

cs.CR↗
arXiv2021

Private Hypothesis Selection

We provide a differentially private algorithm for hypothesis selection. Given samples from an unknown probability distribution $P$ and a set of $m$ probability distributions $\mathcal{H}$, the goal is to output, in a $\varepsilon$-differentially private manner, a distribution from $\mathcal{H}$ whose total variation distance to $P$ is comparable to that of the best such distribution (which we denote by $α$). The sample complexity of our basic algorithm is $O\left(\frac{\log m}{α^2} + \frac{\log m}{α\varepsilon}\right)$, representing a minimal cost for privacy when compared to the non-private algorithm. We also can handle infinite hypothesis classes $\mathcal{H}$ by relaxing to $(\varepsilon,δ)$-differential privacy. We apply our hypothesis selection algorithm to give learning algorithms for a number of natural distribution classes, including Gaussians, product distributions, sums of independent random variables, piecewise polynomials, and mixture classes. Our hypothesis selection procedure allows us to generically convert a cover for a class to a learning algorithm, complementing known learning lower bounds which are in terms of the size of the packing number of the class. As the covering and packing numbers are often closely related, for constant $α$, our algorithms achieve the optimal sample complexity for many classes of interest. Finally, we describe an application to private distribution-free PAC learning.

cs.DS↗