Distributed Multiagent Convex Optimization Over Random Digraphs

Alaviani, Seyyed Shaho; Elia, Nicola

doi:10.1109/tac.2019.2937499

Cited by 27 publications

(13 citation statements)

References 47 publications

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“…It can be then asserted that the operators F i 's are all nonexpansive [19]. As a result, it is easy to verify that problem ( 13) is equivalent to finding fixed points of the operator F := ∑ N i=1 F i /N, which is exactly the same as (2).…”

Section: Distributed Gradient Descent Algorithmmentioning

confidence: 97%

“…For problem (2), if there exists a global computing unit who knows the exact information F, then one famous centralized algorithm, called the KM iteration [8,28], can be used…”

Section: The D-km Iterationmentioning

confidence: 99%

“…This subsection is concerned with developing another distributed algorithm for handling problem (2). In reality, it may be computationally expensive or prohibitive to compute the whole coordinates of F i at a point for i ∈ [N].…”

Section: The D-bkm Iterationmentioning

confidence: 99%

“…It should be noticed that the aforesaid works are only concerned with the Euclidean space. With regard to the Hilbert space, distributed optimization was considered under random communication digraphs in [2], and the common fixed point seeking problem was taken into account for a finite collection of nonexpansive operators in [17], where two distributed algorithms, namely the distributed inexact KM iteration and distributed inexact block-coordinate KM iteration, were proposed. It can be observed that, in [17], it is assumed that there exists at least one common fixed point for all local operators, which motivates the further investigation on the case without any common fixed point for all local operators.…”

Section: Introductionmentioning

confidence: 99%

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Distributed Algorithms for Computing a Fixed Point of Multi-Agent Nonexpansive Operators

Xie

2019

Preprint

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This paper investigates the problem of finding a fixed point for a global nonexpansive operator under time-varying communication graphs in real Hilbert spaces, where the global operator is separable and composed of an aggregate sum of local nonexpansive operators. Each local operator is only privately accessible to each agent, and all agents constitute a network. To seek a fixed point of the global operator, it is indispensable for agents to exchange local information and update their solution cooperatively. To solve the problem, two algorithms are developed, called distributed Krasnosel'skiȋ-Mann (D-KM) and distributed block-coordinate Krasnosel'skiȋ-Mann (D-BKM) iterations, for which the D-BKM iteration is a block-coordinate version of the D-KM iteration in the sense of randomly choosing and computing only one block-coordinate of local operators at each time for each agent. It is shown that the proposed two algorithms can both converge weakly to a fixed point of the global operator. Meanwhile, the designed algorithms are applied to recover the classical distributed gradient descent (DGD) algorithm, devise a new block-coordinate DGD algorithm, handle a distributed shortest distance problem in the Hilbert space for the first time, and solve linear algebraic equations in a novel distributed approach. Finally, the theoretical results are corroborated by a few numerical examples.

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Section: Distributed Gradient Descent Algorithmmentioning

confidence: 97%

“…For problem (2), if there exists a global computing unit who knows the exact information F, then one famous centralized algorithm, called the KM iteration [8,28], can be used…”

Section: The D-km Iterationmentioning

confidence: 99%

Section: The D-bkm Iterationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Distributed Algorithms for Computing a Fixed Point of Multi-Agent Nonexpansive Operators

Xie

2019

Preprint

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“…Example 1.1 (Asynchronous distributed optimization). The line of research into stochastic operators that perform updates randomly has found fruitful application in distributed optimization, where a set of agents cooperate towards the solution of a problem, but the updates may be performed asynchronously and with different precision [9,36,1,3]. Consider a distributed system with N agents, where each agent has a local cost function f i : R → R. Assuming that agents are connected through a communication network, one may be interested in developing a distributed algorithm for solving the following optimization problem:…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Operator Framework for Inexact Static and Online Optimization

Bastianello¹,

Madden²,

Carli³

et al. 2021

Preprint

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This paper provides a unified stochastic operator framework to analyze the convergence of iterative optimization algorithms for both static problems and online optimization and learning. In particular, the framework is well suited for algorithms that are implemented in an inexact or stochastic fashion because of (i) stochastic errors emerging in algorithmic steps, and because (ii) the algorithm may feature random coordinate updates. To this end, the paper focuses on separable operators of the form T x = (T 1 x, . . . , Tnx), defined over the direct sum of possibly infinite-dimensional Hilbert spaces, and investigates the convergence of the associated stochastic Banach-Picard iteration. Results in terms of convergence in mean and in high-probability are presented when the errors affecting the operator follow a sub-Weibull distribution and when updates T i x are performed based on a Bernoulli random variable. In particular, the results are derived for the cases where T is contractive and averaged in terms of convergence to the unique fixed point and cumulative fixed-point residual, respectively. The results do not assume vanishing errors or vanishing parameters of the operator, as typical in the literature (this case is subsumed by the proposed framework), and links with exiting results in terms of almost sure convergence are provided. In the online optimization context, the operator changes at each iteration to reflect changes in the underlying optimization problem. This leads to an online Banach-Picard iteration, and similar results are derived where the bounds for the convergence in mean and high-probability further depend on the evolution of fixed points (i.e., optimal solutions of the time-varying optimization problem).

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Predictive cloud control for nonlinear multiagent systems based on extended state observer and quantizers

Peng,

Yang,

et al. 2024

Intl J Robust & Nonlinear

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In this article, predictive cloud control is investigated for nonlinear networked multiagent system (NMAS) with quantizers via extended state observer (ESO). Considering the network‐induced delays in NMAS, the cloud control scheme is designed. Then, arbitrary region quantizers are used to decrease the quantity of data packets. Moreover, the ESO that can estimate the state and uncertainty of nonlinear NMAS is used to obtain the prediction of data packets. Input‐to‐state stability (ISS) can guarantee the validity of ESO. Sufficient conditions that can achieve stability and consistency for NMAS are given by the zoom strategy. The significance of the scheme is verified by simulation results.

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Distributed Multiagent Convex Optimization Over Random Digraphs

Cited by 27 publications

References 47 publications

Distributed Algorithms for Computing a Fixed Point of Multi-Agent Nonexpansive Operators

Distributed Algorithms for Computing a Fixed Point of Multi-Agent Nonexpansive Operators

A Stochastic Operator Framework for Inexact Static and Online Optimization

Predictive cloud control for nonlinear multiagent systems based on extended state observer and quantizers

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