Distributed subgradient methods and quantization effects

Nedić, Angelia; Оlshevsky, А.G.; Ozdaglar, Asuman; Tsitsiklis, John N.

doi:10.1109/cdc.2008.4738860

Cited by 178 publications

(138 citation statements)

References 21 publications

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“…Distributed consensus-based algorithms have been studied in [19], [18], [21], [26], [16], [20], which rely on deterministic consensus schemes, except for [16] where a random consensus scheme is considered. These algorithms have the following limitations in common:…”

Section: Introductionmentioning

confidence: 99%

Asynchronous Broadcast-Based Convex Optimization Over a Network

Nedić

2011

IEEE Trans. Automat. Contr.

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We consider a distributed multi-agent network system where each agent has its own convex objective function, which can be evaluated with stochastic errors. The problem consists of minimizing the sum of the agent functions over a commonly known constraint set, but without a central coordinator and without agents sharing the explicit form of their objectives. We propose an asynchronous broadcast-based algorithm where the communications over the network are subject to random link failures. We investigate the convergence properties of the algorithm for a diminishing (random) stepsize and a constant stepsize, where each agent chooses its own stepsize independently of the other agents. Under some standard conditions on the gradient errors, we establish almost sure convergence of the method to an optimal point for diminishing stepsize. For constant stepsize, we establish some error bounds on the expected distance from the optimal point and the expected function value. We also provide numerical results.

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Section: Introductionmentioning

confidence: 99%

Asynchronous Broadcast-Based Convex Optimization Over a Network

Nedić

2011

IEEE Trans. Automat. Contr.

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285

260

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“…On a broader basis, the algorithm in this paper is related to the distributed (deterministic) consensus-based optimization algorithm proposed in [22], [23] and further studied in [16], [18], [21], [26], [28]. That algorithm is requires the agents to update simultaneously and to coordinate their stepsize choices, which is in contrast with the algorithm discussed in this paper.…”

Section: Introductionmentioning

confidence: 72%

Asynchronous stochastic convex optimization over random networks: Error bounds

Touri

Nedić

Ram

2010

2010 Information Theory and Applications Workshop (ITA)

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Abstract-We consider a distributed multi-agent network system where the goal is to minimize the sum of convex functions, each of which is known (with stochastic errors) to a specific network agent. We are interested in asynchronous algorithms for solving the problem over a connected network where the communications among the agent are random. At each time, a random set of agents communicate and update their information. When updating, an agent uses the (sub)gradient of its individual objective function and its own stepsize value. The algorithm is completely asynchronous as it neither requires the coordination of agent actions nor the coordination of the stepsize values. We investigate the asymptotic error bounds of the algorithm with a constant stepsize for strongly convex and just convex functions. Our error bounds capture the effects of agent stepsize choices and the structure of the agent connectivity graph. The error bound scales at best as m in the number m of agents when the agent objective functions are strongly convex.

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“…More recently, the authors of [16] consider a variant of incremental gradient methods [21] over networks where each node projects its iterate to a grid before sending the iterate to the next node. Similar quantization ideas are considered [17]- [19] in the context of consensus-type subgradient methods [22]. The work in [20] studies the convergence of standard interference function methods for power control in cellular wireless systems where base stations send binary signals to the users optimizing the transmit radio power.…”

Section: A Related Literaturementioning

confidence: 99%

“…, we obtain the bound in Equation (17). The optimal step-size γ = 2 /(Lα 2 BN 3/2 ) comes by maximizing the denominator in Equation (17).…”

Section: A Constant Step-sizementioning

confidence: 99%

Convergence of Limited Communication Gradient Methods

Magnússon

Enyioha

et al. 2018

IEEE Trans. Automat. Contr.

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Abstract-Distributed optimization increasingly plays a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the complete potential of the technology has not yet been fully exploited in practice due to communication limitations posed by the real-world infrastructures. This work investigates fundamental properties of distributed optimization based on gradient methods, where gradient information is communicated using limited number of bits. In particular, a general class of quantized gradient methods are studied where the gradient direction is approximated by a finite quantization set. Sufficient and necessary conditions are provided on such a quantization set to guarantee that the methods minimize any convex objective function with Lipschitz continuous gradient and a nonempty and bounded set of optimizers. A lower bound on the cardinality of the quantization set is provided, along with specific examples of minimal quantizations. Convergence rate results are established that connect the fineness of the quantization and the number of iterations needed to reach a predefined solution accuracy. Generalizations of the results to a relevant class of constrained problems using projections are considered. Finally, the results are illustrated by simulations of practical systems.

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Distributed subgradient methods and quantization effects

Cited by 178 publications

References 21 publications

Asynchronous Broadcast-Based Convex Optimization Over a Network

Asynchronous Broadcast-Based Convex Optimization Over a Network

Asynchronous stochastic convex optimization over random networks: Error bounds

Convergence of Limited Communication Gradient Methods

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