Machine learning has begun to play a central role in many applications. A multitude of these applications typically also involve datasets that are distributed across multiple computing devices/machines due to either design constraints (e.g., multiagent systems) or computational/privacy reasons (e.g., learning on smartphone data). Such applications often require the learning tasks to be carried out in a decentralized fashion, in which there is no central server that is directly connected to all nodes. In real-world decentralized settings, nodes are prone to undetected failures due to malfunctioning equipment, cyberattacks, etc., which are likely to crash non-robust learning algorithms. The focus of this paper is on robustification of decentralized learning in the presence of nodes that have undergone Byzantine failures. The Byzantine failure model allows faulty nodes to arbitrarily deviate from their intended behaviors, thereby ensuring designs of the most robust of algorithms. But the study of Byzantine resilience within decentralized learning, in contrast to distributed learning, is still in its infancy. In particular, existing Byzantine-resilient decentralized learning methods either do not scale well to large-scale machine learning models, or they lack statistical convergence guarantees that help characterize their generalization errors. In this paper, a scalable, Byzantine-resilient decentralized machine learning framework termed Byzantine-resilient decentralized gradient descent (BRIDGE) is introduced. Algorithmic and statistical convergence guarantees for one variant of BRIDGE are also provided in the paper for both strongly convex problems and a class of nonconvex problems. In addition, large-scale decentralized learning experiments are used to establish that the BRIDGE framework is scalable and it delivers competitive results for Byzantine-resilient convex and nonconvex learning.
We propose a novel robust aggregation rule for distributed synchronous Stochastic Gradient Descent~(SGD) under a general Byzantine failure model. The attackers can arbitrarily manipulate the data transferred between the servers and the workers in the parameter server~(PS) architecture. We prove the Byzantine resilience of the proposed aggregation rules. Empirical analysis shows that the proposed techniques outperform current approaches for realistic use cases and Byzantine attack scenarios.
International Institute of Information Technology Bangalore（班加罗尔国际信息技术学院）
This paper proposes a Robust Gradient Classification Framework (RGCF) for Byzantine fault tolerance in distributed stochastic gradient descent. The framework consists of a pattern recognition filter which we train to be able to classify individual gradients as Byzantine by using their direction alone. This filter is robust to an arbitrary number of Byzantine workers for convex as well as non-convex optimisation settings, which is a significant improvement on the prior work that is robust to Byzantine faults only when up to 50% of the workers are Byzantine. This solution does not require an est…
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
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., ma…
Australian National University（澳大利亚国立大学）；University of Sydney（悉尼大学）
In distributed learning, a central server trains a model according to updates provided by nodes holding local data samples. In the presence of one or more malicious servers sending incorrect information (a Byzantine adversary), standard algorithms for model training such as stochastic gradient descent (SGD) fail to converge. In this paper, we present a simplified convergence theory for the generic Byzantine Resilient SGD method originally proposed by Blanchard et al. [NeurIPS 2017]. Compared to the existing analysis, we shown convergence to a stationary point in expectation under standard assu…
In this work, we consider the resilience of distributed algorithms based on stochastic gradient descent (SGD) in distributed learning with potentially Byzantine attackers, who could send arbitrary information to the parameter server to disrupt the training process. Toward this end, we propose a new Lipschitz-inspired coordinate-wise median approach (LICM-SGD) to mitigate Byzantine attacks. We show that our LICM-SGD algorithm can resist up to half of the workers being Byzantine attackers, while still converging almost surely to a stationary region in non-convex settings. Also, our LICM-SGD meth…
Distributed Computing Laboratory (DCL), École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院（EPFL）分布式计算实验室（DCL））
Momentum is a variant of gradient descent that has been proposed for its benefits on convergence. In a distributed setting, momentum can be implemented either at the server or the worker side. When the aggregation rule used by the server is linear, commutativity with addition makes both deployments equivalent. Robustness and privacy are however among motivations to abandon linear aggregation rules. In this work, we demonstrate the benefits on robustness of using momentum at the worker side. We first prove that computing momentum at the workers reduces the variance-norm ratio of the gradient es…
Microsoft Research Redmond（微软雷德蒙德研究院）；University of Waterloo（滑铁卢大学）；IST Austria（奥地利科学技术研究所）
We study adversary-resilient stochastic distributed optimization, in which $m$ machines can independently compute stochastic gradients, and cooperate to jointly optimize over their local objective functions. However, an $α$-fraction of the machines are $\textit{Byzantine}$, in that they may behave in arbitrary, adversarial ways. We consider a variant of this procedure in the challenging $\textit{non-convex}$ case. Our main result is a new algorithm SafeguardSGD which can provably escape saddle points and find approximate local minima of the non-convex objective. The algorithm is based on a new…
On the Tradeoff between Privacy Preservation and Byzantine-Robustness in Decentralized Learning
School of Computer Science and Engineering, Sun Yat-Sen University（中山大学计算机科学与工程学院）；Department of Electrical and Computer Engineering, University of California, San Diego（加利福尼亚大学圣地亚哥分校电气与计算机工程系）
Chongqing University（重庆大学）；Nanyang Technological University（南洋理工大学）；University of Alberta（阿尔伯塔大学）
Decentralized learning has gained great popularity to improve learning efficiency and preserve data privacy. Each computing node makes equal contribution to collaboratively learn a Deep Learning model. The elimination of centralized Parameter Servers (PS) can effectively address many issues such as privacy, performance bottleneck and single-point-failure. However, how to achieve Byzantine Fault Tolerance in decentralized learning systems is rarely explored, although this problem has been extensively studied in centralized systems. In this paper, we present an in-depth study towards the Byzanti…
We study stochastic gradient descent (SGD) with local iterations in the presence of malicious/Byzantine clients, motivated by the federated learning. The clients, instead of communicating with the central server in every iteration, maintain their local models, which they update by taking several SGD iterations based on their own datasets and then communicate the net update with the server, thereby achieving communication-efficiency. Furthermore, only a subset of clients communicate with the server, and this subset may be different at different synchronization times. The Byzantine clients may c…
We study distributed stochastic gradient descent (SGD) in the master-worker architecture under Byzantine attacks. We consider the heterogeneous data model, where different workers may have different local datasets, and we do not make any probabilistic assumptions on data generation. At the core of our algorithm, we use the polynomial-time outlier-filtering procedure for robust mean estimation proposed by Steinhardt et al. (ITCS 2018) to filter-out corrupt gradients. In order to be able to apply their filtering procedure in our {\em heterogeneous} data setting where workers compute {\em stochas…
Generalization Error Analysis for Attack-Free and Byzantine-Resilient Decentralized Learning with Data Heterogeneity
School of Computer Science and Engineering, Sun Yat-Sen University（中山大学计算机科学与工程学院）；College of Computer, National University of Defense Technology（国防科技大学计算机学院）
University of California, Los Angeles（加州大学洛杉矶分校）；City University of Hong Kong（香港城市大学）
We study distributed optimization in the presence of Byzantine adversaries, where both data and computation are distributed among $m$ worker machines, $t$ of which may be corrupt. The compromised nodes may collaboratively and arbitrarily deviate from their pre-specified programs, and a designated (master) node iteratively computes the model/parameter vector for generalized linear models. In this work, we primarily focus on two iterative algorithms: Proximal Gradient Descent (PGD) and Coordinate Descent (CD). Gradient descent (GD) is a special case of these algorithms. PGD is typically used in …
We present Garfield, a library to transparently make machine learning (ML) applications, initially built with popular (but fragile) frameworks, e.g., TensorFlow and PyTorch, Byzantine-resilient. Garfield relies on a novel object-oriented design, reducing the coding effort, and addressing the vulnerability of the shared-graph architecture followed by classical ML frameworks. Garfield encompasses various communication patterns and supports computations on CPUs and GPUs, allowing addressing the general question of the very practical cost of Byzantine resilience in SGD-based ML applications. We re…
Distributed machine learning algorithms enable learning of models from datasets that are distributed over a network without gathering the data at a centralized location. While efficient distributed algorithms have been developed under the assumption of faultless networks, failures that can render these algorithms nonfunctional occur frequently in the real world. This paper focuses on the problem of Byzantine failures, which are the hardest to safeguard against in distributed algorithms. While Byzantine fault tolerance has a rich history, existing work does not translate into efficient and prac…
Distributed multi-task learning provides significant advantages in multi-agent networks with heterogeneous data sources where agents aim to learn distinct but correlated models simultaneously.However, distributed algorithms for learning relatedness among tasks are not resilient in the presence of Byzantine agents. In this paper, we present an approach for Byzantine resilient distributed multi-task learning. We propose an efficient online weight assignment rule by measuring the accumulated loss using an agent's data and its neighbors' models. A small accumulated loss indicates a large similarit…
University of Southern California（南加州大学）；University of California, Riverside（加州大学河滨分校）
Secure federated learning is a privacy-preserving framework to improve machine learning models by training over large volumes of data collected by mobile users. This is achieved through an iterative process where, at each iteration, users update a global model using their local datasets. Each user then masks its local model via random keys, and the masked models are aggregated at a central server to compute the global model for the next iteration. As the local models are protected by random masks, the server cannot observe their true values. This presents a major challenge for the resilience o…
While the last few decades have witnessed a huge body of work devoted to inference and learning in distributed and decentralized setups, much of this work assumes a non-adversarial setting in which individual nodes---apart from occasional statistical failures---operate as intended within the algorithmic framework. In recent years, however, cybersecurity threats from malicious non-state actors and rogue entities have forced practitioners and researchers to rethink the robustness of distributed and decentralized algorithms against adversarial attacks. As a result, we now have a plethora of algor…
In this paper, we consider the Byzantine-robust stochastic optimization problem defined over decentralized static and time-varying networks, where the agents collaboratively minimize the summation of expectations of stochastic local cost functions, but some of the agents are unreliable due to data corruptions, equipment failures or cyber-attacks. The unreliable agents, which are called as Byzantine agents thereafter, can send faulty values to their neighbors and bias the optimization process. Our key idea to handle the Byzantine attacks is to formulate a total variation (TV) norm-penalized app…
We study Byzantine collaborative learning, where $n$ nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and $f < n$ nodes can behave arbitrarily. We prove that collaborative learning is equivalent to a new form of agreement, which we call averaging agreement. In this problem, nodes start each with an initial vector and seek to approximately agree on a common vector, which is close to the average of honest nodes' initial vectors. We present two asynchronous solutions to averaging agreement, each we prove op…
Machine Learning (ML) solutions are nowadays distributed and are prone to various types of component failures, which can be encompassed in so-called Byzantine behavior. This paper introduces LiuBei, a Byzantine-resilient ML algorithm that does not trust any individual component in the network (neither workers nor servers), nor does it induce additional communication rounds (on average), compared to standard non-Byzantine resilient algorithms. LiuBei builds upon gradient aggregation rules (GARs) to tolerate a minority of Byzantine workers. Besides, LiuBei replicates the parameter server on mult…
Distributed model training is vulnerable to byzantine system failures and adversarial compute nodes, i.e., nodes that use malicious updates to corrupt the global model stored at a parameter server (PS). To guarantee some form of robustness, recent work suggests using variants of the geometric median as an aggregation rule, in place of gradient averaging. Unfortunately, median-based rules can incur a prohibitive computational overhead in large-scale settings, and their convergence guarantees often require strong assumptions. In this work, we present DRACO, a scalable framework for robust distri…
Machine Learning (ML) solutions are nowadays distributed, according to the so-called server/worker architecture. One server holds the model parameters while several workers train the model. Clearly, such architecture is prone to various types of component failures, which can be all encompassed within the spectrum of a Byzantine behavior. Several approaches have been proposed recently to tolerate Byzantine workers. Yet all require trusting a central parameter server. We initiate in this paper the study of the ``general'' Byzantine-resilient distributed machine learning problem where no individu…
Byzantine-Robust Gossip: Insights from a Dual Approach
Center for Applied Mathematics（应用数学中心）；École polytechnique（巴黎高等理工学院）；IP Paris Palaiseau（巴黎-Palaiseau研究所）；Inria（法国国家信息与自动化技术研究所）；Center of Grenoble Alpes University（格勒诺布尔阿尔卑斯大学中心）；CNRS, LJK（国家科学研究中心，LJK）
To improve the resilience of distributed training to worst-case, or Byzantine node failures, several recent approaches have replaced gradient averaging with robust aggregation methods. Such techniques can have high computational costs, often quadratic in the number of compute nodes, and only have limited robustness guarantees. Other methods have instead used redundancy to guarantee robustness, but can only tolerate limited number of Byzantine failures. In this work, we present DETOX, a Byzantine-resilient distributed training framework that combines algorithmic redundancy with robust aggregati…
Increasingly machine learning systems are being deployed to edge servers and devices (e.g. mobile phones) and trained in a collaborative manner. Such distributed/federated/decentralized training raises a number of concerns about the robustness, privacy, and security of the procedure. While extensive work has been done in tackling with robustness, privacy, or security individually, their combination has rarely been studied. In this paper, we propose a secure two-server protocol that offers both input privacy and Byzantine-robustness. In addition, this protocol is communication-efficient, fault-…
