Distributed learning has become a hot research topic due to its wide application in clusterbased large-scale learning, federated learning, edge computing and so on. Most traditional distributed learning methods typically assume no failure or attack. However, many unexpected cases, such as communication failure and even malicious attack, may happen in real applications. Hence, Byzantine learning (BL), which refers to distributed learning with failure or attack, has recently attracted much attention. Most existing BL methods are synchronous, which are impractical in some applications due to heterogeneous or offline workers. In these cases, asynchronous BL (ABL) is usually preferred. In this paper, we propose a novel method, called buffered asynchronous stochastic gradient descent (BASGD), for ABL. To the best of our knowledge, BASGD is the first ABL method that can resist non-omniscient attacks without storing any instances on server. Furthermore, we also propose an improved variant of BASGD, called BASGD with momentum (BASGDm), by introducing momentum into BASGD. BASGDm can resist both non-omniscient and omniscient attacks. Compared with those methods which need to store instances on server, BASGD and BASGDm have a wider scope of application. Both BASGD and BASGDm are compatible with various aggregation rules. Moreover, both BASGD and BASGDm are proved to be convergent and be able to resist failure or attack. Empirical results show that our methods significantly outperform existing ABL baselines when there exists failure or attack on workers.
Recently, new defense techniques have been developed to tolerate Byzantine failures for distributed machine learning. The Byzantine model captures workers that behave arbitrarily, including malicious and compromised workers. In this paper, we break two prevailing Byzantine-tolerant techniques. Specifically we show robust aggregation methods for synchronous SGD -- coordinate-wise median and Krum -- can be broken using new attack strategies based on inner product manipulation. We prove our results theoretically, as well as show empirical validation.
We propose three new robust aggregation rules 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 properties of these aggregation rules. Empirical analysis shows that the proposed techniques outperform current approaches for realistic use cases and Byzantine attack scenarios.
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…
This paper considers the Byzantine fault-tolerance problem in distributed stochastic gradient descent (D-SGD) method - a popular algorithm for distributed multi-agent machine learning. In this problem, each agent samples data points independently from a certain data-generating distribution. In the fault-free case, the D-SGD method allows all the agents to learn a mathematical model best fitting the data collectively sampled by all agents. We consider the case when a fraction of agents may be Byzantine faulty. Such faulty agents may not follow a prescribed algorithm correctly, and may render tr…
Asynchronous distributed machine learning solutions have proven very effective so far, but always assuming perfectly functioning workers. In practice, some of the workers can however exhibit Byzantine behavior, caused by hardware failures, software bugs, corrupt data, or even malicious attacks. We introduce \emph{Kardam}, the first distributed asynchronous stochastic gradient descent (SGD) algorithm that copes with Byzantine workers. Kardam consists of two complementary components: a filtering and a dampening component. The first is scalar-based and ensures resilience against $\frac{1}{3}$ Byz…
We propose two novel stochastic gradient descent algorithms, ByGARS and ByGARS++, for distributed machine learning in the presence of any number of Byzantine adversaries. In these algorithms, reputation scores of workers are computed using an auxiliary dataset at the server. This reputation score is then used for aggregating the gradients for stochastic gradient descent. The computational complexity of ByGARS++ is the same as the usual distributed stochastic gradient descent method with only an additional inner product computation in every iteration. We show that using these reputation scores …
Distributed learning has become a necessity for training ever-growing models by sharing calculation among several devices. However, some of the devices can be faulty, deliberately or not, preventing the proper convergence. As a matter of fact, the baseline distributed SGD algorithm does not converge in the presence of one Byzantine adversary. In this article we focus on the more robust SignSGD algorithm derived from SGD. We provide an upper bound for the convergence rate of SignSGD proving that this new version is robust to Byzantine adversaries. We implemented SignSGD along with Byzantine str…
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…
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We propose Zeno++, a new robust asynchronous Stochastic Gradient Descent~(SGD) procedure which tolerates Byzantine failures of the workers. In contrast to previous work, Zeno++ removes some unrealistic restrictions on worker-server communications, allowing for fully asynchronous updates from anonymous workers, arbitrarily stale worker updates, and the possibility of an unbounded number of Byzantine workers. The key idea is to estimate the descent of the loss value after the candidate gradient is applied, where large descent values indicate that the update results in optimization progress. We p…
As a promising distributed learning technology, analog aggregation based federated learning over the air (FLOA) provides high communication efficiency and privacy provisioning under the edge computing paradigm. When all edge devices (workers) simultaneously upload their local updates to the parameter server (PS) through commonly shared time-frequency resources, the PS obtains the averaged update only rather than the individual local ones. While such a concurrent transmission and aggregation scheme reduces the latency and communication costs, it unfortunately renders FLOA vulnerable to Byzantin…
Byzantine-Robust Distributed SGD: A Unified Analysis and Tight Error Bounds
School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences（中国科学院大学前沿交叉科学学院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；Ministry of Education Key Laboratory of Mathematics and Information Networks, School of Mathematical Sciences, Beijing University of Posts and Telecommunications（北京邮电大学数学科学学院数学与信息网络教育部重点实验室）
We consider the problem of Byzantine fault-tolerance in federated machine learning. In this problem, the system comprises multiple agents each with local data, and a trusted centralized coordinator. In fault-free setting, the agents collaborate with the coordinator to find a minimizer of the aggregate of their local cost functions defined over their local data. We consider a scenario where some agents ($f$ out of $N$) are Byzantine faulty. Such agents need not follow a prescribed algorithm correctly, and may communicate arbitrary incorrect information to the coordinator. In the presence of Byz…
Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）；National University of Singapore（新加坡国立大学）；Toyota Motor Corporation（丰田汽车公司）；University of Zurich（苏黎世大学）
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…
IST Austria（奥地利科学技术研究所）；Microsoft Research AI（微软研究院AI）；MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）
This paper studies the problem of distributed stochastic optimization in an adversarial setting where, out of the $m$ machines which allegedly compute stochastic gradients every iteration, an $α$-fraction are Byzantine, and can behave arbitrarily and adversarially. Our main result is a variant of stochastic gradient descent (SGD) which finds $\varepsilon$-approximate minimizers of convex functions in $T = \tilde{O}\big( \frac{1}{\varepsilon^2 m} + \frac{α^2}{\varepsilon^2} \big)$ iterations. In contrast, traditional mini-batch SGD needs $T = O\big( \frac{1}{\varepsilon^2 m} \big)$ iterations, …
North Carolina State University（北卡罗来纳州立大学）；Wuhan University（武汉大学）
The recent advances in sensor technologies and smart devices enable the collaborative collection of a sheer volume of data from multiple information sources. As a promising tool to efficiently extract useful information from such big data, machine learning has been pushed to the forefront and seen great success in a wide range of relevant areas such as computer vision, health care, and financial market analysis. To accommodate the large volume of data, there is a surge of interest in the design of distributed machine learning, among which stochastic gradient descent (SGD) is one of the mostly …
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…
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
The growth of data, the need for scalability and the complexity of models used in modern machine learning calls for distributed implementations. Yet, as of today, distributed machine learning frameworks have largely ignored the possibility of arbitrary (i.e., Byzantine) failures. In this paper, we study the robustness to Byzantine failures at the fundamental level of stochastic gradient descent (SGD), the heart of most machine learning algorithms. Assuming a set of $n$ workers, up to $f$ of them being Byzantine, we ask how robust can SGD be, without limiting the dimension, nor the size of the …
While machine learning is going through an era of celebrated success, concerns have been raised about the vulnerability of its backbone: stochastic gradient descent (SGD). Recent approaches have been proposed to ensure the robustness of distributed SGD against adversarial (Byzantine) workers sending poisoned gradients during the training phase. Some of these approaches have been proven Byzantine-resilient: they ensure the convergence of SGD despite the presence of a minority of adversarial workers. We show in this paper that convergence is not enough. In high dimension $d \gg 1$, an adver\-sar…
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.
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…
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…
This report considers the problem of Byzantine fault-tolerance in synchronous parallelized learning that is founded on the parallelized stochastic gradient descent (parallelized-SGD) algorithm. The system comprises a master, and $n$ workers, where up to $f$ of the workers are Byzantine faulty. Byzantine workers need not follow the master's instructions correctly, and might send malicious incorrect (or faulty) information. The identity of the Byzantine workers remains fixed throughout the learning process, and is unknown a priori to the master. We propose two coding schemes, a deterministic sch…
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…
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）
Federated Learning (FL) is a nascent decentralized learning framework under which a massive collection of heterogeneous clients collaboratively train a model without revealing their local data. Scarce communication, privacy leakage, and Byzantine attacks are the key bottlenecks of system scalability. In this paper, we focus on communication-efficient distributed (stochastic) gradient descent for non-convex optimization, a driving force of FL. We propose two algorithms, named {\em Adaptive Stochastic Sign SGD (Ada-StoSign)} and {\em $β$-Stochastic Sign SGD ($β$-StoSign)}, each of which compress…
This paper considers the problem of resilient distributed optimization and stochastic machine learning in a server-based architecture. The system comprises a server and multiple agents, where each agent has a local cost function. The agents collaborate with the server to find a minimum of their aggregate cost functions. We consider the case when some of the agents may be asynchronous and/or Byzantine faulty. In this case, the classical algorithm of distributed gradient descent (DGD) is rendered ineffective. Our goal is to design techniques improving the efficacy of DGD with asynchrony and Byza…
The Blavatnik School of Computer Science（布拉瓦尼克计算机科学学院）；Tel Aviv University（特拉维夫大学）
This work presents a new distributed Byzantine tolerant federated learning algorithm, HoldOut SGD, for Stochastic Gradient Descent (SGD) optimization. HoldOut SGD uses the well known machine learning technique of holdout estimation, in a distributed fashion, in order to select parameter updates that are likely to lead to models with low loss values. This makes it more effective at discarding Byzantine workers inputs than existing methods that eliminate outliers in the parameter-space of the learned model. HoldOut SGD first randomly selects a set of workers that use their private data in order …
Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
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 with both 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 t…
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 …
In this work we study the problem of Byzantine-robust learning when data among clients is heterogeneous. We focus on poisoning attacks targeting the convergence of SGD. Although this problem has received great attention; the main Byzantine defenses rely on the IID assumption causing them to fail when data distribution is non-IID even with no attack. We propose the use of Linear Scalarization (LS) as an enhancing method to enable current defenses to circumvent Byzantine attacks in the non-IID setting. The LS method is based on the incorporation of a trade-off vector that penalizes the suspected…
Aalborg University（奥尔堡大学）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Implementations of SGD on distributed systems create new vulnerabilities, which can be identified and misused by one or more adversarial agents. Recently, it has been shown that well-known Byzantine-resilient gradient aggregation schemes are indeed vulnerable to informed attackers that can tailor the attacks (Fang et al., 2020; Xie et al., 2020b). We introduce MixTailor, a scheme based on randomization of the aggregation strategies that makes it impossible for the attacker to be fully informed. Deterministic schemes can be integrated into MixTailor on the fly without introducing any additional…
