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Convergence Rate Of Distributed Averaging Dynamics And Optimization In Networks
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Book Synopsis Convergence Rate of Distributed Averaging Dynamics and Optimization in Networks by : Angelia Nedić
Download or read book Convergence Rate of Distributed Averaging Dynamics and Optimization in Networks written by Angelia Nedić and published by . This book was released on 2015 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in wired and wireless technology lead to the emergence of large-scale networks such as Internet, wireless mobile ad-hoc networks, swarm robotics, smart-grid, and smart-sensor networks. The advances gave rise to new applications in networks including decentralized resource allocation in multi-agent systems, decentralized control of multi-agent systems, collaborative decision making, decentralized learning and estimation, and decentralized in-network signal processing. The advances also gave birth to new large cyber-physical systems such as sensor and social networks. These network systems are typically spatially distributed over a large area and may consists of hundreds of agents in smart-sensor networks to millions of agents in social networks. As such, they do not possess a central coordinator or a central point for access to the complete system information. This lack of central entity makes the traditional (centralized) optimization and control techniques inapplicable, thus necessitating the development of new distributed computational models and algorithms to support efficient operations over such networks. This tutorial provides an overview of the convergence rate of distributed algorithms for coordination and its relevance to optimization in a system of autonomous agents embedded in a communication network, where each agent is aware of (and can communicate with) its local neighbors only. The focus is on distributed averaging dynamics for consensus problems and its role in consensus-based gradient methods for convex optimization problems, where the network objective function is separable across the constituent agents.
Book Synopsis Distributed Averaging Dynamics and Optimization Over Random Networks by : Adel Aghajan Abdollah
Download or read book Distributed Averaging Dynamics and Optimization Over Random Networks written by Adel Aghajan Abdollah and published by . This book was released on 2021 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study Distributed Averaging Dynamics and its main application, i.e. Distributed Optimization. More specifically, the results of this thesis can be divided into two main parts: 1) Ergodicity of distributed averaging dynamics, and 2) Distributed optimization over dependent random networks. First, we study both discrete-time and continuous-time time-varying distributed averaging dynamics. We show a necessary and a sufficient condition for ergodicity of such dynamics. We extend a well-known result in ergodicity of time-homogeneous (time-invariant) averaging dynamics and we show that ergodicity of a dynamics necessitates that its (directed) infinite flow graph has a spanning rooted tree. Then, we show that if groups of agents are connected using a rooted tree and the averaging dynamics restricted to each group is P* and ergodic, then the dynamics over the whole networks is ergodic. In particular, this provides a general condition for convergence of consensus dynamics where groups of agents capable of reaching consensus follow each other on a time-varying network. Then, we study the averaging-based distributed optimization solvers over random networks for both convex and strongly convex functions. We show a general result on the convergence of such schemes for a broad class of dependent weight-matrix sequences. In addition to implying many of the previously known results on this domain, our work shows the robustness of distributed optimization results to link-failure. Also, it provides a new tool for synthesizing distributed optimization algorithms. To prove our main theorems, we establish new results on the rate of convergence analysis of averaging dynamics and non-averaging dynamics over (dependent) random networks. These secondary results, along with the required martingale-type results to establish them, might be of interest to broader research endeavors in distributed computation over random networks.
Book Synopsis Distributed Optimization: Advances in Theories, Methods, and Applications by : Huaqing Li
Download or read book Distributed Optimization: Advances in Theories, Methods, and Applications written by Huaqing Li and published by Springer Nature. This book was released on 2020-08-04 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a valuable reference guide for researchers in distributed optimization and for senior undergraduate and graduate students alike. Focusing on the natures and functions of agents, communication networks and algorithms in the context of distributed optimization for networked control systems, this book introduces readers to the background of distributed optimization; recent developments in distributed algorithms for various types of underlying communication networks; the implementation of computation-efficient and communication-efficient strategies in the execution of distributed algorithms; and the frameworks of convergence analysis and performance evaluation. On this basis, the book then thoroughly studies 1) distributed constrained optimization and the random sleep scheme, from an agent perspective; 2) asynchronous broadcast-based algorithms, event-triggered communication, quantized communication, unbalanced directed networks, and time-varying networks, from a communication network perspective; and 3) accelerated algorithms and stochastic gradient algorithms, from an algorithm perspective. Finally, the applications of distributed optimization in large-scale statistical learning, wireless sensor networks, and for optimal energy management in smart grids are discussed.
Book Synopsis Introduction to Averaging Dynamics over Networks by : Fabio Fagnani
Download or read book Introduction to Averaging Dynamics over Networks written by Fabio Fagnani and published by Springer. This book was released on 2017-11-09 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with averaging dynamics, a paradigmatic example of network based dynamics in multi-agent systems. The book presents all the fundamental results on linear averaging dynamics, proposing a unified and updated viewpoint of many models and convergence results scattered in the literature. Starting from the classical evolution of the powers of a fixed stochastic matrix, the text then considers more general evolutions of products of a sequence of stochastic matrices, either deterministic or randomized. The theory needed for a full understanding of the models is constructed without assuming any knowledge of Markov chains or Perron–Frobenius theory. Jointly with their analysis of the convergence of averaging dynamics, the authors derive the properties of stochastic matrices. These properties are related to the topological structure of the associated graph, which, in the book’s perspective, represents the communication between agents. Special attention is paid to how these properties scale as the network grows in size. Finally, the understanding of stochastic matrices is applied to the study of other problems in multi-agent coordination: averaging with stubborn agents and estimation from relative measurements. The dynamics described in the book find application in the study of opinion dynamics in social networks, of information fusion in sensor networks, and of the collective motion of animal groups and teams of unmanned vehicles. Introduction to Averaging Dynamics over Networks will be of material interest to researchers in systems and control studying coordinated or distributed control, networked systems or multiagent systems and to graduate students pursuing courses in these areas.
Book Synopsis Convergence Speed in Distributed Consensus and Averaging by : Alexander Olshevsky
Download or read book Convergence Speed in Distributed Consensus and Averaging written by Alexander Olshevsky and published by . This book was released on 2006 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose three new algorithms for the distributed averaging and consensus problems: two for the fixed-graph case, and one for the dynamic-topology case. The convergence times of our fixed-graph algorithms compare favorably with other known methods, while our algorithm for the dynamic-topology case is the first to be accompanied by a polynomial-time bound on the worst-case convergence time.
Book Synopsis Multi-agent Optimization by : Angelia Nedić
Download or read book Multi-agent Optimization written by Angelia Nedić and published by Springer. This book was released on 2018-11-01 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains three well-written research tutorials that inform the graduate reader about the forefront of current research in multi-agent optimization. These tutorials cover topics that have not yet found their way in standard books and offer the reader the unique opportunity to be guided by major researchers in the respective fields. Multi-agent optimization, lying at the intersection of classical optimization, game theory, and variational inequality theory, is at the forefront of modern optimization and has recently undergone a dramatic development. It seems timely to provide an overview that describes in detail ongoing research and important trends. This book concentrates on Distributed Optimization over Networks; Differential Variational Inequalities; and Advanced Decomposition Algorithms for Multi-agent Systems. This book will appeal to both mathematicians and mathematically oriented engineers and will be the source of inspiration for PhD students and researchers.
Book Synopsis Distributed Averaging in Dynamic Networks by : Shreevatsa Rajagopalan
Download or read book Distributed Averaging in Dynamic Networks written by Shreevatsa Rajagopalan and published by . This book was released on 2010 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: The question of computing average of numbers present at nodes in a network in a distributed manner using gossip or message-passing algorithms has been of great recent interest across disciplines -- algorithms, control and robotics, estimation, social networks, etc. It has served as a non-trivial, representative model for an important class of questions arising in these disciplines and thus guiding intellectual progress over the past few decades. In most of these applications, there is inherent dynamics present, such as changes in the network topology in terms of communication links, changes in the values of numbers present at nodes, and nodes joining or leaving. The effect of dynamics in terms of communication links on the design and analysis of algorithms for averaging is reasonably well understood, e.g. [14][2][8][4]. However, little is known about the effect of other forms of dynamics. In this thesis, we study the effect of such types of dynamics in the context of maintaining average in the network. Specifically, we design dynamics-aware message-passing or gossip algorithm that maintains good estimate of average in presence of continuous change in numbers at nodes. Clearly, in presence of such dynamics the best one can hope for is a tradeoff between the accuracy of each node's estimate of the average at each time instant and the rate of dynamics. For our algorithm, we characterize this tradeoff and establish it to be near optimal. The dependence of the accuracy of the algorithm on the rate of dynamics as well as on the underlying graph structure is quantified.
Book Synopsis Distributed Optimization in Networked Systems by : Qingguo Lü
Download or read book Distributed Optimization in Networked Systems written by Qingguo Lü and published by Springer Nature. This book was released on 2023-02-08 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on improving the performance (convergence rate, communication efficiency, computational efficiency, etc.) of algorithms in the context of distributed optimization in networked systems and their successful application to real-world applications (smart grids and online learning). Readers may be particularly interested in the sections on consensus protocols, optimization skills, accelerated mechanisms, event-triggered strategies, variance-reduction communication techniques, etc., in connection with distributed optimization in various networked systems. This book offers a valuable reference guide for researchers in distributed optimization and for senior undergraduate and graduate students alike.
Book Synopsis Emerging Applications of Control and Systems Theory by : Roberto Tempo
Download or read book Emerging Applications of Control and Systems Theory written by Roberto Tempo and published by Springer. This book was released on 2018-02-24 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book celebrates Professor Mathukumalli Vidyasagar’s outstanding achievements in systems, control, robotics, statistical learning, computational biology, and allied areas. The contributions in the book summarize the content of invited lectures given at the workshop “Emerging Applications of Control and Systems Theory” (EACST17) held at the University of Texas at Dallas in late September 2017 in honor of Professor Vidyasagar’s seventieth birthday. These contributions are the work of twenty-eight distinguished speakers from eight countries and are related to Professor Vidyasagar’s areas of research. This Festschrift volume will remain as a permanent scientific record of this event.
Book Synopsis Product of Random Stochastic Matrices and Distributed Averaging by : Behrouz Touri
Download or read book Product of Random Stochastic Matrices and Distributed Averaging written by Behrouz Touri and published by Springer Science & Business Media. This book was released on 2012-03-02 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thesis deals with averaging dynamics in a multiagent networked system, which is a main mechanism for diffusing the information over such networks. It arises in a wide range of applications in engineered physical networks (such as mobile communication and sensor networks), as well as social and economic networks. The thesis provides in depth study of stability and other phenomena characterizing the limiting behavior of both deterministic and random averaging dynamics. By developing new concepts, and using the tools from dynamic system theory and non-negative matrix theory, several novel fundamental results are rigorously developed. These contribute significantly to our understanding of averaging dynamics as well as to non-negative random matrix theory. The exposition, although highly rigorous and technical, is elegant and insightful, and accompanied with numerous illustrative examples, which makes this thesis work easily accessible to those just entering this field and will also be much appreciated by experts in the field.
Book Synopsis Modelling, Analysis, and Control of Networked Dynamical Systems by : Ziyang Meng
Download or read book Modelling, Analysis, and Control of Networked Dynamical Systems written by Ziyang Meng and published by Springer Nature. This book was released on 2021-10-15 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive exploration of new tools for modelling, analysis, and control of networked dynamical systems. Expanding on the authors’ previous work, this volume highlights how local exchange of information and cooperation among neighboring agents can lead to emergent global behaviors in a given networked dynamical system. Divided into four sections, the first part of the book begins with some preliminaries and the general networked dynamical model that is used throughout the rest of the book. The second part focuses on synchronization of networked dynamical systems, synchronization with non-expansive dynamics, periodic solutions of networked dynamical systems, and modulus consensus of cooperative-antagonistic networks. In the third section, the authors solve control problems with input constraint, large delays, and heterogeneous dynamics. The final section of the book is devoted to applications, studying control problems of spacecraft formation flying, multi-robot rendezvous, and energy resource coordination of power networks. Modelling, Analysis, and Control of Networked Dynamical Systems will appeal to researchers and graduate students interested in control theory and its applications, particularly those working in networked control systems, multi-agent systems, and cyber-physical systems. This volume can also be used in advanced undergraduate and graduate courses on networked control systems and multi-agent systems.
Book Synopsis Distributed Optimization, Game and Learning Algorithms by : Huiwei Wang
Download or read book Distributed Optimization, Game and Learning Algorithms written by Huiwei Wang and published by Springer Nature. This book was released on 2021-01-04 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the fundamental theory of distributed optimization, game and learning. It includes those working directly in optimization,-and also many other issues like time-varying topology, communication delay, equality or inequality constraints,-and random projections. This book is meant for the researcher and engineer who uses distributed optimization, game and learning theory in fields like dynamic economic dispatch, demand response management and PHEV routing of smart grids.
Book Synopsis The Role of the Network in Distributed Optimization Algorithms by : Konstantinos Tsianos
Download or read book The Role of the Network in Distributed Optimization Algorithms written by Konstantinos Tsianos and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions of this work can be grouped into four important areas: 1) understanding the communication/computation tradeoff and its effect on scalability with the network size, 2) understanding the limitations of the network and the necessary features that distributed algorithms need to possess to be practical, 3) understanding the effects on convergence of network-induced communication delays and 4) understanding the theoretically achievable convergence rates of distributed algorithms. These areas impact the design and deployment of any consensus-based distributed optimization algorithm. " --
Book Synopsis Asynchronous Subgradient Push by : Mahmoud Assran
Download or read book Asynchronous Subgradient Push written by Mahmoud Assran and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "The need to develop distributed optimization methods is rooted in practical applications involving the processing of data that is naturally distributed, private, or simply too large to store on a single machine. In the past decade, a large number of distributed algorithms for solving large-scale convex optimization problems have been proposed and analyzed in the literature, especially from the perspective of multi-agent systems. Although it is fairly well understood which algorithms have the most desirable theoretical properties, many of the theoretical analyses ignore important practical issues such as asynchronism and communication delays. As a result, it is often the case that algorithms with the most desirable theoretical properties (eg, fastest convergence rates in iterations) do not necessarily have the most desirable properties in practice (eg, fastest convergence rates in time). Based on this observation, we propose a new distributed optimization algorithm termed Asynchronous Subgradient-Push. Through numerical experiments we demonstrate that Asynchronous Subgradient-Push converges faster than the state-of-the-art multi-agent methods in practice, is more robust to failing/stalling agents, and scales better with the network size. Motivated by the method's superior empirical performance, we develop a convergence theory, and, in particular, show that a subsequence of the iterates at each agent converges to a neighbourhood of the global minimum, where the size of the neighbourhood depends on the degree of asynchrony in the multi-agent network. We also implement the state-of-the-art first-order methods compared in this work using the MPI (Message Passing Interface) standard for message-passing in clusters, and make them available to the community. In addition, throughout the process of our analysis we develop some peripheral results concerning an asynchronous version of the Push-Sum algorithm for consensus averaging --- a building block for many of the state-of-the-art distributed optimization methods proposed in the literature --- that are interesting in their own respect. In particular, we show that agents running the Push-Sum consensus-averaging algorithm asynchronously converge to the average of the network R-Linearly, where the constant of geometric convergence depends on the maximum delay and the connectivity of the communication topology, and this convergence holds even in the presence of exogenous perturbations at each agent that seek to derail the consensus process." --
Book Synopsis Distributed Algorithms for Optimization Andvariational Inequality Problems by : Aswin Kannan
Download or read book Distributed Algorithms for Optimization Andvariational Inequality Problems written by Aswin Kannan and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation considers three sets of problems arising from optimization andgame-theoretic problems complicated by the presence of uncertainty, limited information,and problem misspecification. Broadly speaking, the research focuseson developing gradient-based algorithms in networked and uncertain regimes andfocuses on the asymptotics and rate statements of such schemes. Next, we providea short description of each part of this dissertation.The first part of this work considers computation of equilibria associated withNash games that lead to monotone variational inequalities, wherein each playersolves a convex program. Distributed extensions of standard approaches for solvingsuch variational problems are characterized by two challenges: (1) Unless suitableassumptions (such as strong monotonicity) are imposed on the mapping arising inthe specification of the variational inequality, iterative methods often require thesolution to a sequence of regularized problems, a naturally two-timescale processthat is harder to implement in practice; (2) Additionally, algorithm parametersfor all players (such as steplengths, regularization parameters, etc.) have to bechosen centrally and communicated to all players; importantly, these parameterscannot be independently chosen by a player. Motivated by these shortcomings,we present two practically implementable distributed regularization schemes thatwork on a single-timescale; specifically, each scheme requires precisely one gradientor projection step at every iteration. Both schemes are characterized by the propertythat the regularization/centering parameter are updated after every iteration,rather than when one has approximately solved the regularized problem. To aidin distributed settings requiring limited coordination across players, the schemesallow players to select their parameters independently and do not insist on centralprescription of such parameters. We conclude with an application of these schemeson a networked Cournot game with nonlinear prices.In the second portion of our work, we consider stochastic variational inequalitiesiiiunder pseudomonotone settings. Referred to as pseudomonotone stochastic variationalinequality problems or PSVIs, such problems emerge from product pricing,fractional optimization problems, and subclasses of economic equilibrium problemsarising in uncertain regimes. Succinctly, we make two sets of contributions to thestudy of PSVIs. In the first part of the paper, we observe that a direct applicationof standard existence/uniqueness theory requires a tractable expression for theintegrals arising from the expectation, a relative rarity when faced with generaldistributions. Instead, we develop integration-free sufficiency conditions for theexistence and uniqueness of solutions to PSVIs. In the second part of the paper, weconsider the solution of PSVIs via stochastic approximation (SA) schemes, motivatedby the observation that almost all of the prior SA schemes can accommodatemonotone SVIs. Under various forms of pseudomonotonicity, we prove that thesolution iterates produced by extragradient SA schemes converge to the solutionset in an almost sure sense. This result is further extended to mirror-prox regimesand an analogous statement is also provided for monotone regimes, under a weaksharpnessrequirement, where prior results have only shown convergence in terms ofthe gap function through the use of averaging. Under strong pseudomonotonicity,we derive the optimal initial steplength and show that the mean-squared error inthe solution iterates produced by the extragradient SA scheme converges at theoptimal rate of O(1/K). Similar rates are derived for mirror-prox generalizations andmonotone SVIs under a weak-sharpness requirement. Finally, both the asymptoticsand the empirical rates of the schemes are studied on a set of pseudomonotone andnon-monotone variational problems.The third part of this dissertation studies networked settings where agentsattempt to solve a common problem, whose information is both misspecified andonly partly known to every agent. We consider a convex optimization problemthat requires minimizing a sum of misspecified agent-specific expectation-valuedconvex functions over the intersection of a collection of agent-specific convex sets,denoted by X1, . . . ,Xm. The agent objectives are misspecified in a parametric senseand this misspecification may be resolved through solving a distinct stochasticconvex learning problem. We consider the simultaneous resolution of both problemsthrough a joint set of schemes in which agents update their decisions and theirbeliefs regarding the misspecified parameter at every step. The former combinesan agent-specific averaging step and a projected stochastic gradient step whileparameter updates are carried out through a projected stochastic gradient step.Given such a set of coupled schemes, we provide both almost sure convergencestatements as well as convergence rate statements when either Xi = X for every ior when X is an intersection over Xi. Notably, we prove that when X is the intersection and agent objectivesare strongly convex, we recover the optimal rate of stochastic approximation ofO(1/K) in the solution iterates despite the presence of averaging (arising fromthe consensus step) and learning (arising from misspecification). When strongconvexity assumptions are weakened to mere convexity but Xi = X for every i, weshow that the averaged sequence over the entire K iterations displays a modestdegradation in the convergence rate from the optimal rate in terms of functionvalue. When the averaging window is reduced to K/2, we recover the optimalrate of convergence in function values. Preliminary numerics are provided for aneconomic dispatch problem with misspecified cost functions.
Book Synopsis Analysis and Design of Distributed Optimization Algorithms by : Akhil Sundararajan
Download or read book Analysis and Design of Distributed Optimization Algorithms written by Akhil Sundararajan and published by . This book was released on 2021 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work concerns the analysis and design of distributed first-order optimization algorithms. The goal of such algorithms is to optimize a global function that is the average of local functions using only local computations and communications. Many recent algorithms have been proposed that achieve linear convergence to the global optimum. We provide a unified analysis that yields the worst-case linear convergence rate as a function of the properties of the functions and underlying network, as well as the parameters of the algorithm. The framework requires solving a small semidefinite program whose feasibility is a sufficient condition for certifying linear convergence of a distributed algorithm. We present results for both known, fixed graphs and unknown, time-varying graphs. The analysis framework is a computationally efficient method for distributed algorithm analysis that enables the rapid comparison, selection, and tuning of algorithms. This work also makes an effort to systematize distributed algorithm design by devising a canonical form for first-order distributed algorithms. The canonical form characterizes any distributed algorithm that can be implemented using a single round of communication and gradient computation per iteration, and where each agent stores up to two state variables. The canonical form features a minimal set of parameters that are both unique and expressive enough to capture any distributed algorithm in this class. Using this canonical form, we propose a new algorithm, which we call SVL, that is easily implementable and achieves a faster worst-case convergence rate than all other known algorithms.
Book Synopsis Distributed Optimization by : Dusan Jakovetic
Download or read book Distributed Optimization written by Dusan Jakovetic and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
