Can Machines Learn Robustly, Privately, and Efficiently?

The success of machine learning (ML) applications relies on vast datasets and distributed architectures, which, as they grow, present challenges for ML. In real-world scenarios, where data often contains sensitive information, issues like data poisoning and hardware failures are common. Ensuring privacy and robustness is vital for the broad adoption of ML in public life. This paper examines the costs associated with achieving these objectives in distributed architectures. We overview the meanings of privacy and robustness in distributed ML, and clarify how they can be achieved efficiently in isolation. However, we contend that the integration of these objectives entails a notable compromise in computational efficiency. We delve into this intricate balance, exploring the challenges and solutions for privacy, robustness, and computational efficiency in ML applications.

Practical Homomorphic Aggregation for Byzantine ML

Due to the large-scale availability of data, machine learning (ML) algorithms are being deployed in distributed topologies, where different nodes collaborate to train ML models over their individual data by exchanging model-related information (e.g., gradients) with a central server. However, distributed learning schemes are notably vulnerable to two threats. First, Byzantine nodes can single-handedly corrupt the learning by sending incorrect information to the server, e.g., erroneous gradients. The standard approach to mitigate such behavior is to use a non-linear robust aggregation method at the server. Second, the server can violate the privacy of the nodes. Recent attacks have shown that exchanging (unencrypted) gradients enables a curious server to recover the totality of the nodes' data. The use of homomorphic encryption (HE), a gold standard security primitive, has extensively been studied as a privacy-preserving solution to distributed learning in non-Byzantine scenarios. However, due to HE's large computational demand especially for high-dimensional ML models, there has not yet been any attempt to design purely homomorphic operators for non-linear robust aggregators. In this work, we present SABLE, the first completely homomorphic and Byzantine robust distributed learning algorithm. SABLE essentially relies on a novel plaintext encoding method that enables us to implement the robust aggregator over batching-friendly BGV. Moreover, this encoding scheme also accelerates state-of-the-art homomorphic sorting with larger security margins and smaller ciphertext size. We perform extensive experiments on image classification tasks and show that our algorithm achieves practical execution times while matching the ML performance of its non-private counterpart.

Distributed Learning with Curious and Adversarial Machines

The ubiquity of distributed machine learning (ML) in sensitive public domain applications calls for algorithms that protect data privacy, while being robust to faults and adversarial behaviors. Although privacy and robustness have been extensively studied independently in distributed ML, their synthesis remains poorly understood. We present the first tight analysis of the error incurred by any algorithm ensuring robustness against a fraction of adversarial machines, as well as differential privacy (DP) for honest machines' data against any other curious entity. Our analysis exhibits a fundamental trade-off between privacy, robustness, and utility. Surprisingly, we show that the cost of this trade-off is marginal compared to that of the classical privacy-utility trade-off. To prove our lower bound, we consider the case of mean estimation, subject to distributed DP and robustness constraints, and devise reductions to centralized estimation of one-way marginals. We prove our matching upper bound by presenting a new distributed ML algorithm using a high-dimensional robust aggregation rule. The latter amortizes the dependence on the dimension in the error (caused by adversarial workers and DP), while being agnostic to the statistical properties of the data.

Fixing by Mixing: A Recipe for Optimal Byzantine ML under Heterogeneity

Byzantine machine learning (ML) aims to ensure the resilience of distributed learning algorithms to misbehaving (or Byzantine) machines. Although this problem received significant attention, prior works often assume the data held by the machines to be homogeneous, which is seldom true in practical settings. Data heterogeneity makes Byzantine ML considerably more challenging, since a Byzantine machine can hardly be distinguished from a non-Byzantine outlier. A few solutions have been proposed to tackle this issue, but these provide suboptimal probabilistic guarantees and fare poorly in practice. This paper closes the theoretical gap, achieving optimality and inducing good empirical results. In fact, we show how to automatically adapt existing solutions for (homogeneous) Byzantine ML to the heterogeneous setting through a powerful mechanism, we call nearest neighbor mixing (NNM), which boosts any standard robust distributed gradient descent variant to yield optimal Byzantine resilience under heterogeneity. We obtain similar guarantees (in expectation) by plugging NNM in the distributed stochastic heavy ball method, a practical substitute to distributed gradient descent. We obtain empirical results that significantly outperform state-of-the-art Byzantine ML solutions.

SoK: On the Impossible Security of Very Large Foundation Models

Large machine learning models, or so-called foundation models, aim to serve as base-models for application-oriented machine learning. Although these models showcase impressive performance, they have been empirically found to pose serious security and privacy issues. We may however wonder if this is a limitation of the current models, or if these issues stem from a fundamental intrinsic impossibility of the foundation model learning problem itself. This paper aims to systematize our knowledge supporting the latter. More precisely, we identify several key features of today's foundation model learning problem which, given the current understanding in adversarial machine learning, suggest incompatibility of high accuracy with both security and privacy. We begin by observing that high accuracy seems to require (1) very high-dimensional models and (2) huge amounts of data that can only be procured through user-generated datasets. Moreover, such data is fundamentally heterogeneous, as users generally have very specific (easily identifiable) data-generating habits. More importantly, users' data is filled with highly sensitive information, and maybe heavily polluted by fake users. We then survey lower bounds on accuracy in privacy-preserving and Byzantine-resilient heterogeneous learning that, we argue, constitute a compelling case against the possibility of designing a secure and privacy-preserving high-accuracy foundation model. We further stress that our analysis also applies to other high-stake machine learning applications, including content recommendation. We conclude by calling for measures to prioritize security and privacy, and to slow down the race for ever larger models.

Making Byzantine Decentralized Learning Efficient

Decentralized-SGD (D-SGD) distributes heavy learning tasks across multiple machines (a.k.a., {\em nodes}), effectively dividing the workload per node by the size of the system. However, a handful of \emph{Byzantine} (i.e., misbehaving) nodes can jeopardize the entire learning procedure. This vulnerability is further amplified when the system is \emph{asynchronous}. Although approaches that confer Byzantine resilience to D-SGD have been proposed, these significantly impact the efficiency of the process to the point of even negating the benefit of decentralization. This naturally raises the question: \emph{can decentralized learning simultaneously enjoy Byzantine resilience and reduced workload per node?} We answer positively by proposing \newalgorithm{} that ensures Byzantine resilience without losing the computational efficiency of D-SGD. Essentially, \newalgorithm{} weakens the impact of Byzantine nodes by reducing the variance in local updates using \emph{Polyak's momentum}. Then, by establishing coordination between nodes via {\em signed echo broadcast} and a {\em nearest-neighbor averaging} scheme, we effectively tolerate Byzantine nodes whilst distributing the overhead amongst the non-Byzantine nodes. To demonstrate the correctness of our algorithm, we introduce and analyze a novel {\em Lyapunov function} that accounts for the {\em non-Markovian model drift} arising from the use of momentum. We also demonstrate the efficiency of \newalgorithm{} through experiments on several image classification tasks.

Byzantine Machine Learning Made Easy by Resilient Averaging of Momentums

Byzantine resilience emerged as a prominent topic within the distributed machine learning community. Essentially, the goal is to enhance distributed optimization algorithms, such as distributed SGD, in a way that guarantees convergence despite the presence of some misbehaving (a.k.a., {\em Byzantine}) workers. Although a myriad of techniques addressing the problem have been proposed, the field arguably rests on fragile foundations. These techniques are hard to prove correct and rely on assumptions that are (a) quite unrealistic, i.e., often violated in practice, and (b) heterogeneous, i.e., making it difficult to compare approaches. We present \emph{RESAM (RESilient Averaging of Momentums)}, a unified framework that makes it simple to establish optimal Byzantine resilience, relying only on standard machine learning assumptions. Our framework is mainly composed of two operators: \emph{resilient averaging} at the server and \emph{distributed momentum} at the workers. We prove a general theorem stating the convergence of distributed SGD under RESAM. Interestingly, demonstrating and comparing the convergence of many existing techniques become direct corollaries of our theorem, without resorting to stringent assumptions. We also present an empirical evaluation of the practical relevance of RESAM.

Combining Differential Privacy and Byzantine Resilience in Distributed SGD

Privacy and Byzantine resilience (BR) are two crucial requirements of modern-day distributed machine learning. The two concepts have been extensively studied individually but the question of how to combine them effectively remains unanswered. This paper contributes to addressing this question by studying the extent to which the distributed SGD algorithm, in the standard parameter-server architecture, can learn an accurate model despite (a) a fraction of the workers being malicious (Byzantine), and (b) the other fraction, whilst being honest, providing noisy information to the server to ensure differential privacy (DP). We first observe that the integration of standard practices in DP and BR is not straightforward. In fact, we show that many existing results on the convergence of distributed SGD under Byzantine faults, especially those relying on $(\alpha,f)$-Byzantine resilience, are rendered invalid when honest workers enforce DP. To circumvent this shortcoming, we revisit the theory of $(\alpha,f)$-BR to obtain an approximate convergence guarantee. Our analysis provides key insights on how to improve this guarantee through hyperparameter optimization. Essentially, our theoretical and empirical results show that (1) an imprudent combination of standard approaches to DP and BR might be fruitless, but (2) by carefully re-tuning the learning algorithm, we can obtain reasonable learning accuracy while simultaneously guaranteeing DP and BR.