Resilient Distributed Optimization Algorithms for Resource Allocation

Uribe, César A.; Wai, Hoi-To; Alizadeh, Mahnoosh

doi:10.1109/cdc40024.2019.9030051

Cited by 5 publications

(2 citation statements)

References 25 publications

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“…where f i is the local smooth objective function of agent i and h is a non-smooth regularization term that is shared across all the agents. Problem (1) is referred to as decentralized convex composite optimization [1], [2] and finds broad applications in optimal control of multi-agent systems [3], resource allocation [4], and large-scale machine learning [5], just to name a few.…”

Section: Introductionmentioning

confidence: 99%

Decentralized Composite Optimization in Stochastic Networks: A Dual Averaging Approach with Linear Convergence

Shi¹,

Zhou²,

Pei³

et al. 2021

Preprint

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Decentralized optimization, particularly the class of decentralized composite convex optimization (DCCO) problems, has found many applications. Due to ubiquitous communication congestion and random dropouts in practice, it is highly desirable to design decentralized algorithms that can handle stochastic communication networks. However, most existing algorithms for DCCO only work in time-invariant networks and cannot be extended to stochastic networks because they inherently need knowledge of network topology a priori. In this paper, we propose a new decentralized dual averaging (DDA) algorithm that can solve DCCO in stochastic networks. Under a rather mild condition on stochastic networks, we show that the proposed algorithm attains global linear convergence if each local objective function is strongly convex. Our algorithm substantially improves the existing DDA-type algorithms as the latter were only known to converge sublinearly prior to our work. The key to achieving the improved rate is the design of a novel dynamic averaging consensus protocol for DDA, which intuitively leads to more accurate local estimates of the global dual variable. To the best of our knowledge, this is the first linearly convergent DDA-type decentralized algorithm and also the first algorithm that attains global linear convergence for solving DCCO in stochastic networks. Numerical results are also presented to support our design and analysis.

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Section: Introductionmentioning

confidence: 99%

Decentralized Composite Optimization in Stochastic Networks: A Dual Averaging Approach with Linear Convergence

Shi¹,

Zhou²,

Pei³

et al. 2021

Preprint

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show abstract

“…The present paper is a revised and extended version of the preliminary conference report [31]. This paper expands [31] into multiple attack scenarios and includes numerical studies. Paper Organization: The remainder of the paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Resilient Primal-Dual Optimization Algorithms for Distributed Resource Allocation

Turan,

Uribe,

Wai

et al. 2020

Preprint

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Distributed algorithms for multi-agent resource allocation can provide privacy and scalability over centralized algorithms in many cyber-physical systems. However, the distributed nature of these algorithms can render these systems vulnerable to man-in-the-middle attacks that can lead to nonconvergence and infeasibility of resource allocation schemes. In this paper, we propose attack-resilient distributed algorithms based on primal-dual optimization when Byzantine attackers are present in the system. In particular, we design attack-resilient primal-dual algorithms for static and dynamic impersonation attacks by means of robust statistics. For static impersonation attacks, we formulate a robustified optimization model and show that our algorithm guarantees convergence to a neighborhood of the optimal solution of the robustified problem. On the other hand, a robust optimization model is not required for the dynamic impersonation attack scenario and we are able to design an algorithm that is shown to converge to a near-optimal solution of the original problem. We analyze the performances of our algorithms through both theoretical and computational studies.

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Decentralized Composite Optimization in Stochastic Networks: A Dual Averaging Approach With Linear Convergence

Pei

Zhang

Shi

2023

IEEE Trans. Automat. Contr.

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Resilient Distributed Optimization Algorithms for Resource Allocation

Cited by 5 publications

References 25 publications

Decentralized Composite Optimization in Stochastic Networks: A Dual Averaging Approach with Linear Convergence

Decentralized Composite Optimization in Stochastic Networks: A Dual Averaging Approach with Linear Convergence

Resilient Primal-Dual Optimization Algorithms for Distributed Resource Allocation

Decentralized Composite Optimization in Stochastic Networks: A Dual Averaging Approach With Linear Convergence

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