Given a set of robots with arbitrary initial location and no agreement on a global coordinate system, convergence requires that all robots asymptotically approach the exact same, but unknown beforehand, location. Robots are oblivious-- they do not recall the past computations -- and are allowed to move in a one-dimensional space. Additionally, robots cannot communicate directly, instead they obtain system related information only via visual sensors. We draw a connection between the convergence problem in robot networks, and the distributed \emph{approximate agreement} problem (that requires correct processes to decide, for some constant $ε$, values distance $ε$ apart and within the range of initial proposed values). Surprisingly, even though specifications are similar, the convergence implementation in robot networks requires specific assumptions about synchrony and Byzantine resilience. In more details, we prove necessary and sufficient conditions for the convergence of mobile robots despite a subset of them being Byzantine (i.e. they can exhibit arbitrary behavior). Additionally, we propose a deterministic convergence algorithm for robot networks and analyze its correctness and complexity in various synchrony settings. The proposed algorithm tolerates f Byzantine robots for (2f+1)-sized robot networks in fully synchronous networks, (3f+1)-sized in semi-synchronous networks. These bounds are optimal for the class of cautious algorithms, which guarantee that correct robots always move inside the range of positions of the correct robots.
Distributed Learning often suffers from Byzantine failures, and there have been a number of works studying the problem of distributed stochastic optimization under Byzantine failures, where only a portion of workers, instead of all the workers in a distributed learning system, compute stochastic gradients at each iteration. These methods, albeit workable under Byzantine failures, have the shortcomings of either a sub-optimal convergence rate or high computation cost. To this end, we propose a new Byzantine-resilient stochastic gradient descent algorithm (BrSGD for short) which is provably robu…
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…
Shandong University（山东大学）；University of Chinese Academy of Sciences（中国科学院大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；City University of Hong Kong（香港城市大学）
Both Byzantine resilience and communication efficiency have attracted tremendous attention recently for their significance in edge federated learning. However, most existing algorithms may fail when dealing with real-world irregular data that behaves in a heavy-tailed manner. To address this issue, we study the stochastic convex and non-convex optimization problem for federated learning at edge and show how to handle heavy-tailed data while retaining the Byzantine resilience, communication efficiency and the optimal statistical error rates simultaneously. Specifically, we first present a Byzan…
Stanford University（斯坦福大学）；University of Pennsylvania（宾夕法尼亚大学）；University of Wisconsin（威斯康星大学）
There has been a growing need to provide Byzantine-resilience in distributed model training. Existing robust distributed learning algorithms focus on developing sophisticated robust aggregators at the parameter servers, but pay less attention to balancing the communication cost and robustness. In this paper, we propose Solon, an algorithmic framework that exploits gradient redundancy to provide communication efficiency and Byzantine robustness simultaneously. Our theoretical analysis shows a fundamental trade-off among computational load, communication cost, and Byzantine robustness. We also d…
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…
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…
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 malfunctio…
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…
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…
In this work, we consider the distributed stochastic optimization problem of minimizing a non-convex function $f(x) = \mathbb{E}_{ξ\sim \mathcal{D}} f(x; ξ)$ in an adversarial setting, where the individual functions $f(x; ξ)$ can also be potentially non-convex. We assume that at most $α$-fraction of a total of $K$ nodes can be Byzantines. We propose a robust stochastic variance-reduced gradient (SVRG) like algorithm for the problem, where the batch gradients are computed at the worker nodes (WNs) and the stochastic gradients are computed at the server node (SN). For the non-convex optimization…
The accelerated digitalisation of society along with technological evolution have extended the geographical span of cyber-physical systems. Two main threats have made the reliable and real-time control of these systems challenging: (i) uncertainty in the communication infrastructure induced by scale, and heterogeneity of the environment and devices; and (ii) targeted attacks maliciously worsening the impact of the above-mentioned communication uncertainties, disrupting the correctness of real-time applications. This paper addresses those challenges by showing how to build distributed protocols…
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 consensus is a key enabler for many distributed systems including distributed databases and blockchains. Canopus is a scalable distributed consensus protocol that ensures that live nodes in a system agree on an ordered sequence of operations (called transactions). Unlike most prior consensus protocols, Canopus does not rely on a single leader. Instead, it uses a virtual tree overlay for message dissemination to limit network traffic across oversubscribed links. It leverages hardware redundancies, both within a rack and inside the network fabric, to reduce both protocol complexity a…
The problem of Byzantine consensus has been key to designing secure distributed systems. However, it is particularly difficult, mainly due to the presence of Byzantine processes that act arbitrarily and the unknown message delays in general networks. Although it is well known that both safety and liveness are at risk as soon as $n/3$ Byzantine processes fail, very few works attempted to characterize precisely the faults that produce safety violations from the faults that produce termination violations. In this paper, we present a new lower bound on the solvability of the consensus problem by d…
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）
We present two distributed algorithms for the {\em Byzantine counting problem}, which is concerned with estimating the size of a network in the presence of a large number of Byzantine nodes. In an $n$-node network ($n$ is unknown), our first algorithm, which is {\em deterministic}, finishes in $O(\log{n})$ rounds and is time-optimal. This algorithm can tolerate up to $O(n^{1 - γ})$ arbitrarily (adversarially) placed Byzantine nodes for any arbitrarily small (but fixed) positive constant $γ$. It outputs a (fixed) constant factor estimate of $\log{n}$ that would be known to all but $o(1)$ fracti…
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…
With upcoming blockchain infrastructures, world-spanning Byzantine consensus is getting practical and necessary. In geographically distributed systems, the pace at which consensus is achieved is limited by the heterogenous latencies of connections between replicas. If deployed on a wide-area network, consensus-based systems benefit from weighted replication, an approach that utilizes extra replicas and assigns higher voting power to well connected replicas. This enables more choice in quorum formation and replicas can leverage proportionally smaller quorums to advance, thus decreasing consensu…
Traditional resilient systems operate on fully-replicated fault-tolerant clusters, which limits their scalability and performance. One way to make the step towards resilient high-performance systems that can deal with huge workloads, is by enabling independent fault-tolerant clusters to efficiently communicate and cooperate with each other, as this also enables the usage of high-performance techniques such as sharding and parallel processing. Recently, such inter-cluster communication was formalized as the Byzantine cluster-sending problem, and worst-case optimal protocols have been proposed t…
Automated Byzantine-Resilient Clustered Decentralized Federated Learning for Battery Intelligence in Connected EVs
SAMOVAR, Télécom SudParis（SAMOVAR，法国电信南巴黎学院）；Department of Computer Science, German University of Technology in Oman (GUtech)（阿曼技术大学计算机科学系）；L3i, La Rochelle University（拉罗什大学L3i）
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…
Byzantine Fault Tolerance (BFT) enables correct operation of distributed, i.e., replicated applications in the face of malicious take-over and faulty/buggy individual instances. Recently, BFT designs have gained traction in the context of Software Defined Networking (SDN). In SDN, controller replicas are distributed and their state replicated for high availability purposes. Malicious controller replicas, however, may destabilize the control plane and manipulate the data plane, thus motivating the BFT requirement. Nonetheless, deploying BFT in practice comes at a disadvantage of increased traff…
