Asynchronous Multiagent Primal-Dual Optimization

Hale, Matthew; Nedić, Angelia; Egerstedt, Magnus

doi:10.1109/tac.2017.2662019

Cited by 39 publications

(28 citation statements)

References 22 publications

(30 reference statements)

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“…A saddle-point method for distributed, continuous-time, online optimization is proposed in [127]. An asynchronous, primal-dual, cloud-based algorithm for distributed convex optimization is provided in [128]. An asynchronous algorithm which allows the presence of local nonconvex constraints is presented in [129].…”

Section: Discussion and Referencesmentioning

confidence: 99%

Distributed Optimization for Smart Cyber-Physical Networks

Notarstefano¹,

Notarnicola²,

Camisa³

2019

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The presence of embedded electronics and communication capabilities as well as sensing and control in smart devices has given rise to the novel concept of cyber-physical networks, in which agents aim at cooperatively solving complex tasks by local computation and communication. Numerous estimation, learning, decision and control tasks in smart networks involve the solution of large-scale, structured optimization problems in which network agents have only a partial knowledge of the whole problem. Distributed optimization aims at designing local computation and communication rules for the network processors allowing them to cooperatively solve the global optimization problem without relying on any central unit. The purpose of this survey is to provide an introduction to distributed optimization methodologies. Principal approaches, namely (primal) consensus-based, duality-based and constraint exchange methods, are formalized. An analysis of the basic schemes is supplied, and state-of-the-art extensions are reviewed.

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Section: Discussion and Referencesmentioning

confidence: 99%

Distributed Optimization for Smart Cyber-Physical Networks

Notarstefano¹,

Notarnicola²,

Camisa³

2019

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“…The convergence of Algorithm 1 will be measured using a block-maximum norm as in [25], [14], and [24].…”

Section: A Block-maximum Normsmentioning

confidence: 99%

Totally Asynchronous Distributed Quadratic Programming with Independent Stepsizes and Regularizations

Ubl

Hale

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Quadratic programs arise in robotics, communications, smart grids, and many other applications. As these problems grow in size, finding solutions becomes much more computationally demanding, and new algorithms are needed to efficiently solve them. Targeting large-scale problems, we develop a multi-agent quadratic programming framework in which each agent updates only a small number of the total decision variables in a problem. Agents communicate their updated values to each other, though we do not impose any restrictions on the timing with which they do so, nor on the delays in these transmissions. Furthermore, we allow weak parametric coupling among agents, in the sense that they are free to independently choose their stepsizes, subject to mild restrictions. We show that these stepsize restrictions depend upon a problem's condition number. We further provide the means for agents to independently regularize the problem they solve, thereby improving condition numbers and, as we will show, convergence properties, while preserving agents' independence in selecting parameters. Simulation results are provided to demonstrate the success of this framework on a practical quadratic program. I. INTRODUCTIONConvex optimization problems arise in a diverse array of engineering applications, including signal processing [1], robotics [2], [3], communications [4], machine learning [5], and many others [6]. In all of these areas, problems can become very large as the number of network members (robots, processors, etc.) becomes large. Accordingly, there has arisen interest in solving large-scale optimization problems. A common feature of large-scale solvers is that they are parallelized or distributed among a collection of agents in some way. As the number of agents grows, it can be difficult or impossible to ensure synchrony among distributed computations and communications, and there has therefore arisen interest in distributed asynchronous optimization algorithms.One line of research considers asynchronous optimization algorithms in which agents' communication topologies vary in time. A representative sample of this work includes [7]- [12], and these algorithms all rely on an underlying averaging-based update law, i.e., different agents update the same decision variables and then repeatedly average their iterates to mitigate disagreements that stem from asynchrony. These approaches (and others in the literature) require some form of graph connectivity over intervals of a finite length. In this paper, we are interested in cases in which delay bounds are outside agents' control, e.g., due to environmental hazards and adversarial jamming

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“…Work in [17] was expanded upon in [19], where it was shown that a fixed Tikhonov regularization implies the existence of the nested sets required in [17] for asymptotic convergence. However, developments in [19] require every agent to apply the same regularization, which can be difficult to enforce and verify in practice, especially in large decentralized networks. Moreover, convergence in [19] is measured with respect to the same un-weighted norm for all agents.…”

Section: Introductionmentioning

confidence: 99%

“…However, developments in [19] require every agent to apply the same regularization, which can be difficult to enforce and verify in practice, especially in large decentralized networks. Moreover, convergence in [19] is measured with respect to the same un-weighted norm for all agents. There is a wide variety of statistical and machine learning problems which must be normalized due to disparate numerical scales across potentially many orders of magnitude [20], and which may require measuring convergence of different components in different norms.…”

Section: Introductionmentioning

confidence: 99%

Asynchronous Distributed Optimization with Heterogeneous Regularizations and Normalizations

Hochhaus

Hale

2018

2018 IEEE Conference on Decision and Control (CDC)

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As multi-agent networks grow in size and scale, they become increasingly difficult to synchronize, though agents must work together even when generating and sharing different information at different times. Targeting such cases, this paper presents an asynchronous optimization framework in which the time between successive communications and computations is unknown and unspecified for each agent. Agents' updates are carried out in blocks, with each agent updating only a small subset of all decision variables. To provide robustness to asynchrony, each agent uses an independently chosen Tikhonov regularization. Convergence is measured with respect to a weighted block-maximum norm in which convergence of agents' blocks can be measured in different p-norms and weighted differently to heterogeneously normalize problems. Asymptotic convergence is shown and convergence rates are derived explicitly in terms of a problem's parameters, with only mild restrictions imposed upon them. Simulation results are provided to verify the theoretical developments made.The authors are with the

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Asynchronous Multiagent Primal-Dual Optimization

Cited by 39 publications

References 22 publications

Distributed Optimization for Smart Cyber-Physical Networks

Distributed Optimization for Smart Cyber-Physical Networks

Totally Asynchronous Distributed Quadratic Programming with Independent Stepsizes and Regularizations

Asynchronous Distributed Optimization with Heterogeneous Regularizations and Normalizations

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