Robust federated learning aims to maintain reliable performance despite the presence of adversarial or misbehaving workers. While state-of-the-art (SOTA) robust distributed gradient descent (Robust-DGD) methods were proven theoretically optimal, their empirical success has often relied on pre-aggregation gradient clipping. However, existing static clipping strategies yield inconsistent results: enhancing robustness against some attacks while being ineffective or even detrimental against others. To address this limitation, we propose a principled adaptive clipping strategy, Adaptive Robust Clipping (ARC), which dynamically adjusts clipping thresholds based on the input gradients. We prove that ARC not only preserves the theoretical robustness guarantees of SOTA Robust-DGD methods but also provably improves asymptotic convergence when the model is well-initialized. Extensive experiments on benchmark image classification tasks confirm these theoretical insights, demonstrating that ARC significantly enhances robustness, particularly in highly heterogeneous and adversarial settings.

The possibility of adversarial (a.k.a., Byzantine) clients makes federated learning (FL) prone to arbitrary manipulation. The natural approach to robustify FL against adversarial clients is to replace the simple averaging operation at the server in the standard $\mathsf{FedAvg}$ algorithm by a robust averaging rule. While a significant amount of work has been devoted to studying the convergence of federated robust averaging (which we denote by $\mathsf{FedRo}$), prior work has largely ignored the impact of client subsampling and local steps, two fundamental FL characteristics. While client subsampling increases the effective fraction of Byzantine clients, local steps increase the drift between the local updates computed by honest (i.e., non-Byzantine) clients. Consequently, a careless deployment of $\mathsf{FedRo}$ could yield poor performance. We validate this observation by presenting an in-depth analysis of $\mathsf{FedRo}$ tightly analyzing the impact of client subsampling and local steps. Specifically, we present a sufficient condition on client subsampling for nearly-optimal convergence of $\mathsf{FedRo}$ (for smooth non-convex loss). Also, we show that the rate of improvement in learning accuracy diminishes with respect to the number of clients subsampled, as soon as the sample size exceeds a threshold value. Interestingly, we also observe that under a careful choice of step-sizes, the learning error due to Byzantine clients decreases with the number of local steps. We validate our theory by experiments on the FEMNIST and CIFAR-$10$ image classification tasks.

Federated Learning (FL) is an appealing approach to training machine learning models without sharing raw data. However, standard FL algorithms are iterative and thus induce a significant communication cost. One-Shot FL (OFL) trades the iterative exchange of models between clients and the server with a single round of communication, thereby saving substantially on communication costs. Not surprisingly, OFL exhibits a performance gap in terms of accuracy with respect to FL, especially under high data heterogeneity. We introduce Fens, a novel federated ensembling scheme that approaches the accuracy of FL with the communication efficiency of OFL. Learning in Fens proceeds in two phases: first, clients train models locally and send them to the server, similar to OFL; second, clients collaboratively train a lightweight prediction aggregator model using FL. We showcase the effectiveness of Fens through exhaustive experiments spanning several datasets and heterogeneity levels. In the particular case of heterogeneously distributed CIFAR-10 dataset, Fens achieves up to a $26.9$% higher accuracy over SOTA OFL, being only $3.1$% lower than FL. At the same time, Fens incurs at most $4.3\times$ more communication than OFL, whereas FL is at least $10.9\times$ more communication-intensive than Fens.

Federated learning (FL) is an appealing paradigm that allows a group of machines (a.k.a. clients) to learn collectively while keeping their data local. However, due to the heterogeneity between the clients’ data distributions, the model obtained through the use of FL algorithms may perform poorly on some client’s data. Personalization addresses this issue by enabling each client to have a different model tailored to their own data while simultaneously benefiting from the other clients’ data. We consider an FL setting where some clients can be adversarial, and we derive conditions under which full collaboration fails. Specifically, we analyze the generalization performance of an interpolated personalized FL framework in the presence of adversarial clients, and we precisely characterize situations when full collaboration performs strictly worse than fine-tuned personalization. Our analysis determines how much we should scale down the level of collaboration, according to data heterogeneity and the tolerable fraction of adversarial clients. We support our findings with empirical results on mean estimation and binary classification problems, considering synthetic and benchmark image classification datasets

The success of machine learning (ML) has been intimately linked with the availability of large amounts of data, typically collected from heterogeneous sources and processed on vast networks of computing devices (also called workers). Beyond accuracy, the use of ML in critical domains such as healthcare and autonomous driving calls for robustness against data poisoning and faulty workers. The problem of Byzantine ML formalizes these robustness issues by considering a distributed ML environment in which workers (storing a portion of the global dataset) can deviate arbitrarily from the prescribed algorithm. Although the problem has attracted a lot of attention from a theoretical point of view, its practical importance for addressing realistic faults (where the behavior of any worker is locally constrained) remains unclear. It has been argued that the seemingly weaker threat model where only workers' local datasets get poisoned is more reasonable. We highlight here some important results on the efficacy of Byzantine robustness for tackling data poisoning. In particular, we discuss cases where, while tolerating a wider range of faulty behaviors, Byzantine ML yields solutions that are optimal even under the weaker threat model of data poisoning.

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.

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. 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.

Collaborative learning algorithms, such as distributed SGD (or D-SGD), are prone to faulty machines that may deviate from their prescribed algorithm because of software or hardware bugs, poisoned data or malicious behaviors. While many solutions have been proposed to enhance the robustness of D-SGD to such machines, previous works either resort to strong assumptions (trusted server, homogeneous data, specific noise model) or impose a gradient computational cost that is several orders of magnitude higher than that of D-SGD. We present MoNNA, a new algorithm that (a) is provably robust under standard assumptions and (b) has a gradient computation overhead that is linear in the fraction of faulty machines, which is conjectured to be tight. Essentially, MoNNA uses Polyak’s momentum of local gradients for local updates and nearest-neighbor averaging (NNA) for global mixing, respectively. While MoNNA is rather simple to implement, its analysis has been more challenging and relies on two key elements that may be of independent interest. Specifically, we introduce the mixing criterion of $(\alpha, \lambda)$-reduction to analyze the non-linear mixing of non-faulty machines, and present a way to control the tension between the momentum and the model drifts. We validate our theory by experiments on image classification and make our code available at https://github.com/LPD-EPFL/robust-collaborative-learning.

The theory underlying robust distributed learning algorithms, designed to resist adversarial machines, matches empirical observations when data is homogeneous. Under data heterogeneity however, which is the norm in practical scenarios, established lower bounds on the learning error are essentially vacuous and greatly mismatch empirical observations. This is because the heterogeneity model considered is too restrictive and does not cover basic learning tasks such as least-squares regression. We consider in this paper a more realistic heterogeneity model, namely $(G,B)$-gradient dissimilarity, and show that it covers a larger class of learning problems than existing theory. Notably, we show that the breakdown point under heterogeneity is lower than the classical fraction $\frac{1}{2}$. We also prove a new lower bound on the learning error of any distributed learning algorithm. We derive a matching upper bound for a robust variant of distributed gradient descent, and empirically show that our analysis reduces the gap between theory and practice.

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., 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 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: resilient averaging at the server and 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.

The increasing prevalence of personal devices motivates the design of algorithms that can leverage their computing power, together with the data they generate, in order to build privacy-preserving and effective machine learning models. However, traditional distributed learning algorithms impose a uniform workload on all participating devices, most often discarding the weakest participants. This not only induces a suboptimal use of available computational resources, but also significantly reduces the quality of the learning process, as data held by the slowest devices is discarded from the procedure. This paper proposes HgO, a distributed learning scheme with parameterizable iteration costs that can be adjusted to the computational capabilities of different devices. HgO encourages the participation of slower devices, thereby improving the accuracy of the model when the participants do not share the same dataset. When combined with a robust aggregation rule, HgO can tolerate some level of Byzantine behavior, depending on the hardware profile of the devices (we prove, for the first time, a trade-off between Byzantine tolerance and hardware heterogeneity). We also demonstrate the convergence of HgO, theoretically and empirically, without assuming any specific partitioning of the data over the devices. We present an exhaustive set of experiments, evaluating the performance of HgO on several classification tasks and highlighting the importance of incorporating slow devices when learning in a Byzantine-prone environment with heterogeneous participants.

This paper considers the problem of Byzantine fault-tolerance in distributed multi-agent optimization. In this problem, each agent has a local cost function, and in the fault-free case, the goal is to design a distributed algorithm that allows all the agents to find a minimum point of all the agents' aggregate cost function. We consider a scenario where some agents might be Byzantine faulty that renders the original goal of computing a minimum point of all the agents' aggregate cost vacuous. A more reasonable objective for an algorithm in this scenario is to allow all the non-faulty agents to compute the minimum point of only the non-faulty agents' aggregate cost. Prior work shows that if there are up to f (out of n) Byzantine agents then a minimum point of the non-faulty agents' aggregate cost can be computed exactly if and only if the non-faulty agents' costs satisfy a certain redundancy property called 2f-redundancy. However, 2f-redundancy is an ideal property that can be satisfied only in systems free from noise or uncertainties, which can make the goal of exact fault-tolerance unachievable in some applications. Thus, we introduce the notion of (f,ε)-resilience, a generalization of exact fault-tolerance wherein the objective is to find an approximate minimum point of the non-faulty aggregate cost, with ε accuracy. This approximate fault-tolerance can be achieved under a weaker condition that is easier to satisfy in practice, compared to 2f-redundancy. We obtain necessary and sufficient conditions for achieving (f, ε)-resilience characterizing the correlation between relaxation in redundancy and approximation in resilience. In case when the agents' cost functions are differentiable, we obtain conditions for (f, ε)-resilience of the distributed gradient-descent method when equipped with robust gradient aggregation; such as comparative gradient elimination or coordinate-wise trimmed mean.

This paper addresses the problem of combining Byzantine resilience with privacy in machine learning (ML). Specifically, we study if a distributed implementation of the renowned Stochastic Gradient Descent (SGD) learning algorithm is feasible withboth differential privacy (DP) and (α,f)-Byzantine resilience. To the best of our knowledge, this is the first work to tackle this problem from a theoretical point of view. A key finding of our analyses is that the classical approaches to these two (seemingly) orthogonal issues are incompatible. More precisely, we show that a direct composition of these techniques makes the guarantees of the resulting SGD algorithm depend unfavourably upon the number of parameters of the ML model, making the training of large models practically infeasible. We validate our theoretical results through numerical experiments on publicly-available datasets; showing that it is impractical to ensure DP and Byzantine resilience simultaneously.

This paper considers the problem of Byzantine fault-tolerance in distributed multi-agent optimization. In this problem, each agent has a local cost function. The goal of a distributed optimization algorithm is to allow the agents to collectively compute a minimum of their aggregate cost function. We consider the case when a certain number of agents may be Byzantine faulty. Such faulty agents may not follow a prescribed algorithm, and they may send arbitrary or incorrect information regarding their local cost functions. Unless a fault-tolerance mechanism is employed, traditional distributed optimization algorithms cannot tolerate such faulty agents.