Distributed Stopping Criterion for Ratio Consensus

Prakash, Mangal; Talukdar, Saurav; Attree, Sandeep; Patel, Sourav; Salapaka, Murti V.

doi:10.1109/allerton.2018.8635839

Cited by 12 publications

(12 citation statements)

References 14 publications

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“…To this end, we propose a distributed gradient-descent method to solve problem (2) over directed graphs. Our scheme is a combination of a finite-time consensus protocol of [23] and the gradient descent method. We will refer to our protocol as gradient-consensus method.…”

Section: Problem Formulationmentioning

confidence: 99%

Gradient-Consensus Method for Distributed Optimization in Directed Multi-Agent Networks

Khatana

Saraswat

Patel

et al. 2020

2020 American Control Conference (ACC)

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In this article, a distributed optimization problem for minimizing a sum, n i=1 f i , of convex objective functions, f i , is addressed. Here each function f i is a function of n variables, private to agent i which defines the agent's objective. Agents can only communicate locally with neighbors defined by a communication network topology. These f i 's are assumed to be Lipschitz-differentiable convex functions. For solving this optimization problem, we develop a novel distributed algorithm, which we term as the gradient-consensus method. The gradient-consensus scheme uses a finite-time terminated consensus protocol called ρ-consensus, which allows each local estimate to be ρ-close to each other at every iteration. The parameter ρ is a fixed constant which can be determined independently of the network size or topology. It is shown that the estimate of the optimal solution at any local agent i converges geometrically to the optimal solution within O(ρ) where ρ can be chosen to be arbitrarily small.

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Section: Problem Formulationmentioning

confidence: 99%

Gradient-Consensus Method for Distributed Optimization in Directed Multi-Agent Networks

Khatana

Saraswat

Patel

et al. 2020

2020 American Control Conference (ACC)

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“…To realize distributed stopping when the precision of iterations has met the requirement, we utilize the max/minconsensus-based stopping mechanism in [29] after the K 2th iteration. Note that the scheme in [29] deals with static digraphs, but it can be easily extended to the settings with time-varying digraphs, given that in this case the max/min consensus protocols can still converge in finite time. The following assumption is required by this mechanism.…”

Section: B Privacy-preserving Information Disseminationmentioning

confidence: 99%

Private and Robust Distributed Nonconvex Optimization via Polynomial Approximation

He¹,

He²,

Chen³

et al. 2021

Preprint

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There has been work on exploiting polynomial approximation to solve distributed nonconvex optimization problems. This idea facilitates arbitrarily precise global optimization without requiring local evaluations of gradients at every iteration. Nonetheless, there remains a gap between existing theoretical guarantees and diverse practical requirements for dependability, including privacy preservation and robustness to network imperfections (e.g., time-varying directed communication, asynchrony and packet drops). To fill this gap and keep the above strengths, we propose a Dependable Chebyshev-Proxy-based distributed Optimization Algorithm (D-CPOA). Specifically, to ensure both accuracy of solutions and privacy preservation of local objective functions, a new privacy-preserving mechanism is designed. This mechanism leverages the randomness in block-wise insertions of perturbed data and separate subtractions of added noises, and its effects are thoroughly analyzed through (α, β)-data-privacy. In addition, to gain robustness to various network imperfections, we use the push-sum consensus protocol as a backbone, discuss its specific enhancements, and evaluate the performance of the proposed algorithm accordingly. Thanks to the linear consensusbased structure of iterations, we avoid the privacy-accuracy trade-off and the bother of selecting appropriate step-sizes in different settings. We provide rigorous treatments of the accuracy, dependability and complexity. It is shown that the advantages brought by the idea of polynomial approximation are perfectly maintained when all the above challenging requirements exist. Simulations demonstrate the efficacy of the developed algorithm.

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“…j∈V x j (0) = N α (as j∈V y j (0) = N ). It is sufficient to prove that under the attack strategy (9) j∈V x j (k) = N α − N θ. Consider i to be the intruder node and let k 1 , k 2 , .…”

Section: Data Manipulation Attacksmentioning

confidence: 99%

“…In this section, we propose a cyber-secured framework for networks running distributed consensus algorithms. We first present the max-min protocols to obtain global maximum and minimum values of the network and use the monotonicity property of these protocols [9] to devise the proposed distributed intruder detection algorithm. Define the maximum and minimum value of the ratio of numerator and denominator states given by (1a) and (1b) over all nodes at any time instant k as, for all nodes j ∈ N + i .…”

Section: Frameworkmentioning

confidence: 99%

See 1 more Smart Citation

Distributed Detection of Malicious Attacks on Consensus Algorithms with Applications in Power Networks

Patel

Khatana

Saraswat

et al. 2020

2020 7th International Conference on Control, Decision and Information Technologies (CoDIT)

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Consensus-based distributed algorithms are well suited for coordination among agents in a cyber-physical system. These distributed schemes, however, suffer from their vulnerability to cyber attacks that are aimed at manipulating data and control flow. In this article, we present a novel distributed method for detecting the presence of such intrusions for a distributed multi-agent system following ratio consensus. We employ a Max-Min protocol to develop low cost, easy to implement detection strategies where each participating node detects the intrusion independently, eliminating the need for a trusted certifying agent in the network. The effectiveness of the detection method is demonstrated by numerical simulations on a 1000 node network to demonstrate the efficacy and simplicity of implementation.

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Distributed Stopping Criterion for Ratio Consensus

Cited by 12 publications

References 14 publications

Gradient-Consensus Method for Distributed Optimization in Directed Multi-Agent Networks

Gradient-Consensus Method for Distributed Optimization in Directed Multi-Agent Networks

Private and Robust Distributed Nonconvex Optimization via Polynomial Approximation

Distributed Detection of Malicious Attacks on Consensus Algorithms with Applications in Power Networks

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