Iterative Byzantine Vector Consensus in Incomplete Graphs

Vaidya, Nitin H.

doi:10.1007/978-3-642-45249-9_2

Cited by 55 publications

(57 citation statements)

References 14 publications

(47 reference statements)

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“…We briefly summarize the aspects of correctness proof of Algorithm 2 from [28] that are necessary for our subsequent discussion. By using the Tverberg points in the update of v i t above, effectively, the extreme message values (that may potentially be sent by faulty agents) are trimmed away.…”

Section: Correctness Of Algorithm Byz-itermentioning

confidence: 99%

Defending non-Bayesian learning against adversarial attacks

Vaidya

2018

Distrib. Comput.

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This paper addresses the problem of non-Bayesian learning over multi-agent networks, where agents repeatedly collect partially informative observations about an unknown state of the world, and try to collaboratively learn the true state. We focus on the impact of the adversarial agents on the performance of consensus-based non-Bayesian learning, where non-faulty agents combine local learning updates with consensus primitives. In particular, we consider the scenario where an unknown subset of agents suffer Byzantine faults -agents suffering Byzantine faults behave arbitrarily.We propose two learning rules.-In our first update rule, each agent updates its local beliefs as (up to normalization) the product of (1) the likelihood of the cumulative private signals and (2) the weighted geometric average of the beliefs of its incoming neighbors and itself. Under reasonable assumptions on the underlying network structure and the global identifiability of the network, we show that all the non-faulty agents asymptotically agree on the true state almost surely. For the case when every agent is failure-free, we show that (with high probability) each agent's beliefs on the wrong hypotheses decrease at rate O(exp(−Ct 2 )), where t is the number of iterations, and C is a constant. -In general when agents may be adversarial, network identifiability condition specified for the above learning rule scales poorly in the number of state candidates m. In addition, the computation complexity per agent per iteration of this learning rule is forbiddingly high. Thus, we propose a modification of our first learning rule, whose complexity per iteration per agent is O(m 2 n log n), where n is the number of agents in the network. We show that this modified learning rule works under a much weaker network identifiability condition. In addition, this new condition is independent of m.⋆

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Section: Correctness Of Algorithm Byz-itermentioning

confidence: 99%

Defending non-Bayesian learning against adversarial attacks

Vaidya

2018

Distrib. Comput.

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“…Approximate agreement has also been studied in dynamic networks [Charron-Bost et al 2015;Li et al 2012Li et al , 2014]. -Byzantine Vector Consensus (BVC) reaches consensus when inputs are vectors under complete graphs [Vaidya and Garg 2013] and incomplete graphs [Vaidya 2014]. Mendes and Herlihy [2013] studied the multidimensional approximate agreement in asynchronous systems, where the agreement definition is different: the distance used in multidimensional approximate agreement is Euclidean distance.…”

Section: Introductionmentioning

confidence: 99%

On Precision Bound of Distributed Fault-Tolerant Sensor Fusion Algorithms

Wang

et al. 2016

ACM Comput. Surv.

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Sensors have limited precision and accuracy. They extract data from the physical environment, which contains noise. The goal of sensor fusion is to make the final decision robust, minimizing the influence of noise and system errors. One problem that has not been adequately addressed is establishing the bounds of fusion result precision. Precision is the maximum range of disagreement that can be introduced by one or more faulty inputs. This definition of precision is consistent both with Lamport's Byzantine Generals problem and the mini-max criteria commonly found in game theory. This article considers the precision bounds of several fault-tolerant information fusion approaches, including Byzantine agreement, Marzullo's interval-based approach, and the Brooks-Iyengar fusion algorithm. We derive precision bounds for these fusion algorithms. The analysis provides insight into the limits imposed by fault tolerance and guidance for applying fusion approaches to applications. . 2016. On precision bound of distributed fault-tolerant sensor fusion algorithms.

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“…Recognition of this has motivated us to achieve a resilient convex combination, which refers to the convex combination of normal states that have not been manipulated by cyber-attacks, only knowing the upper bound to the number of malicious agents. Such a resilient convex combination could be achieved by recently developed methodologies based on Tverberg points [15,21,22,28,30], which are however computationally expensive. Thus one major goal of this paper is to develop an algorithm with low computational complexity for achieving a resilient convex combination.…”

Section: Introductionmentioning

confidence: 99%

“…Thus in this paper, we invest methods which can also be applied into the non-trivial case when 0 < κ < m − σ. One way to achieve a resilient convex combination is through Tverberg points as in [15,28,30]. For any S ⊂ A, let H(x S ) denote the convex hull of vectors in x S , that is,…”

Section: Introductionmentioning

confidence: 99%

“…Tverberg Theorem [29]: Suppose m ≥ κ(n + 1) + 1 for the given set x A . Then there must exist a partition of A into κ + 1 disjoint subsets B 1 , · · · , B κ+1 such that While results in [15,22,28,30] are elegant, one major concern of applying Tverberg points lies in the requirement of high computational complexity. As mentioned in [1,18], except for some specific values of n, the computational complexity of calculating Tverberg points grows exponentially with the dimension n. In the following, we will develop a low-complexity algorithm for achieving resilient convex combinations based on the intersection of convex hulls.…”

Section: Introductionmentioning

confidence: 99%

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A resilient convex combination for consensus-based distributed algorithms

Wang¹,

Mou²,

Sundaram³

2019

Numerical Algebra, Control &Amp; Optimization

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Consider a set of vectors in R n , partitioned into two classes: normal vectors and malicious vectors. The number of malicious vectors is bounded but their identities are unknown. The paper provides a way for achieving a resilient convex combination, which is a convex combination of only normal vectors. Compared with existing approaches based on Tverberg points, the proposed method based on the intersection of convex hulls has lower computational complexity. Simulations suggest that the proposed method can be applied to resilience for consensus-based distributed algorithms against Byzantine attacks.

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Iterative Byzantine Vector Consensus in Incomplete Graphs

Cited by 55 publications

References 14 publications

Defending non-Bayesian learning against adversarial attacks

Defending non-Bayesian learning against adversarial attacks

On Precision Bound of Distributed Fault-Tolerant Sensor Fusion Algorithms

A resilient convex combination for consensus-based distributed algorithms

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