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A distributed Algorithm for Solving Linear Algebraic Equations Over Random Networks

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2021年第5期66卷 2399-2406页

作者： Alaviani, Seyyed Shaho Elia, Nicola Iowa State Univ Ames IA 50011 USA Clemson Univ Dept Mech Engn Clemson SC 29634 USA Univ Minnesota Dept Elect & Comp Engn Minneapolis MN 55455 USA

This article considers the problem of solving linear algebraic equations of the form Ax=b among multiagents, which seek a solution by using local information in presence of random communication topologies. The equation is solved by m agents where each agent only knows a subset of rows of the partitioned matrix [A,b]. The problem is formulated such that this formulation does not need the distribution of random interconnection graphs. Therefore, this framework includes asynchronous updates and/or unreliable communication protocols. The random Krasnoselskii-Mann iterative algorithm is applied that converges almost surely and in mean square to a solution of the problem for any matrices A and b and any initial conditions of agents' states. The algorithm is a totally asynchronous algorithm without requiring a priori B-connectivity and distribution dependency assumptions. The algorithm is able to solve the problem even if the weighted matrix of the graph is periodic and irreducible for synchronous protocol. It is demonstrated that the limit point to which the agents' states converge is determined by the unique solution of a convex optimization problem regardless of the distribution of random communication graphs. Finally, some numerical examples are given to show the results.

关键词： Mathematical model Protocols Hilbert space distributed algorithms Convex functions Network topology Topology Asynchronous distributed algorithm linear algebraic equations random graphs

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distributed Stochastic Optimization in Networks With Low Informational Exchange

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第5期67卷 2989-3008页

作者： Li, Wenjie Assaad, Mohamad CentraleSupelec Lab Signaux & Syst F-91190 Gif Sur Yvette France Univ Paris Saclay Lab Signaux & Syst L2S CentraleSupelec IIMR CNRS 8506 F-91190 Gif Sur Yvette France

We consider a distributed stochastic optimization problem in networks with finite number of nodes. Each node adjusts its action to optimize the global utility of the network, which is defined as the sum of local utilities of all nodes. While Gradient descent method is a common technique to solve such optimization problem, the computation of the gradient may require much information exchange. In this paper, we consider that each node can only have a noisy numerical observation of its local utility, of which the closed-form expression is not available. This assumption is quite realistic, especially when the system is either too complex or constantly changing. Nodes may exchange partially the observation of their local utilities to estimate the global utility at each timeslot. We propose a distributed algorithm based on stochastic perturbation, under the assumption that each node has only part of the local utilities of the other nodes. We use stochastic approximation tools to prove that our algorithm converges almost surely to the optimum, given that the objective function is smooth and strictly concave. The convergence rate is also derived, under the additional assumption of strongly concave objective function. It is shown that the convergence rate scales as O (K-0.5) after a sufficient number of iterations K > K-0, which is the optimal rate order in terms of K for our problem. Although the proposed algorithm can be applied to general optimization problems, we perform simulations for a typical power control problem in wireless networks and present numerical results to corroborate our claims.

关键词： Optimization derivative-free optimization stochastic approximation convergence analysis distributed algorithms

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distributed Constrained Optimization Over Unbalanced Directed Networks Using Asynchronous Broadcast-Based Algorithm

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2021年第3期66卷 1102-1115页

作者： Li, Huaqing Lu, Qingguo Chen, Guo Huang, Tingwen Dong, Zhaoyang Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligen Chongqing 400715 Peoples R China Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia Texas A&M Univ Qatar Sci Program Doha 23874 Qatar

This article focuses on distributed convex optimization problems over an unbalanced directed multiagent (no central coordinator) network with inequality constraints. The goal is to cooperatively minimize the sum of all locally known convex cost functions. Every single agent in the network only knows its local objective function and local inequality constraint, and is constrained to a privately known convex set. Furthermore, we particularly discuss the scenario in which the interactions among agents over the whole network are subjected to possible link failures. To collaboratively solve the optimization problem, we mainly concentrate on an epigraph form of the original constrained optimization to overcome the unbalancedness of directed networks, and propose a new distributed asynchronous broadcast-based optimization algorithm. The algorithm allows that not only the updates of agents are asynchronous in a distributed fashion, but also the step-sizes of all agents are uncoordinated. An important characteristic of the proposed algorithm is to cope with the constrained optimization problem in the case of unbalanced directed networks whose communications are subjected to possible link failures. Under two standard assumptions that the communication network is directly strongly connected and the subgradients of all local objective functions are bounded, we provide an explicit analysis for convergence of the algorithm. Simulation results obtained by three numerical experiments substantiate the feasibility of the algorithm and validate the theoretical findings.

关键词： Signal processing algorithms Convex functions Linear programming Convergence distributed algorithms Cost function Asynchronous algorithm distributed convex optimization epigraph form inequality constraints unbalanced directed networks

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distributed and Resilient Planning-Control for Optimal LEO Satellite Constellation Coverage

Distributed and Resilient Planning-Control for Optimal LEO S...

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American Control Conference (ACC)

作者： Zhao, Yuhan Zhu, Quanyan New York Univ Dept Elect & Comp Engn New York NY 10003 USA

ISBN: (数字)9781665451963

ISBN: (纸本)9781665451963

Coverage services provided by LEO satellite constellations have served as the base platform for various space applications. However, the surge of space attacks such as physical and cyber attacks are greatly endangering the security of satellite constellations and the integrity of the coverage services. As repairs of satellites are challenging, a distributed protection mechanism is necessary to ensure the self-healing of the satellite constellation coverage from different attacks. To this end, this paper establishes a distributed framework to empower a resilient satellite constellation coverage design and control within a single orbit. Each satellite can make decisions individually to recover from adversarial and non-adversarial attacks and keep providing coverage service. We first provide the average coverage cost to measure the coverage performance. Then, we formulate the joint resilient coverage planning-control problem as a two-stage problem by decoupling the coverage planning and fuel-optimal control. A distributed algorithm is proposed to find the optimal coverage configuration. The multi-waypoint MPC methodology is adopted to steer satellites to the target configuration. Finally, we use a typical LEO satellite constellation as a case study to corroborate the results.

关键词： Space vehicles Satellite constellations Satellites Low earth orbit satellites Surge protection Orbits distributed algorithms

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distributed strategies for mixed equilibrium problems: Continuous-time theoretical approaches

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AUTOMATICA 2024年 161卷

作者： Lu, Kaihong Wang, Hongxia Zhu, Qixin Shandong Univ Sci & Technol Coll Elect Engn & Automat Qingdao 266590 Peoples R China Suzhou Univ Sci & Technol Sch Mech Engn Suzhou 215009 Peoples R China

In this paper, the mixed equilibrium problem is studied by employing a continuous-time multi-agent system, where the objective of agents is to cooperatively find a point from the feasible set such that the sum of bifunctions with a free-variable is nonnegative. Different from existing works on mixed equilibrium problems with only convex set constraints, we consider a more general case where the feasible set is constrained by a set of convex inequalities. Moreover, each agent only has access to the information of its own bifunction and inequality constraint function, as well as the information of a local convex set. To handle this problem, the Karush-Kuhn-Tucker condition that is suitable for continuous-time theoretical approaches is provided, and a continuous-time distributed primal-dual algorithm is proposed. Under mild assumptions on the graph and bifunctions, we prove that the states of all agents asymptotically converge to the common solution of the mixed equilibrium problem. Finally, a simulation example is worked out to demonstrate the effectiveness of our theoretical results. (c) 2023 Elsevier Ltd. All rights reserved.

关键词： Multi-agent systems Mixed equilibrium problems Inequality constraints distributed algorithms

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distributed Access Control for Collaborative Applications using CRDTs 9

Distributed Access Control for Collaborative Applications us...

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Proceedings of the 9th Principles and Practice of Consistency for distributed Data (PaPoC)

作者： Rault, Pierre-Antoine Ignat, Claudia-Lavinia Perrin, Olivier Univ Lorraine CNRS Inria LORIA F-54000 Nancy France

ISBN: (纸本)9781450392563

distributed applications are part of our everyday lives, but too often their good operation depends on central servers, all potential points of failure and performance bottlenecks. Designing systems for fully distributed communications however still requires porting common mechanisms needed for feature-rich modern applications such as user rights differentiation, multiple administrators, and end-to-end encryption. We propose a distributed access control mechanism for collaborative applications by relying on conflict-free replicated data types (CRDT), and design an access control policy CRDT able to support Google Docs and POSIX file systems as example of distributed applications. To enforce that policy, we outline a generic data model, examine different conflict resolution strategies at the data and policy levels, and consider a novel approach towards conflicts between data and policy operations.

关键词： distributed algorithms access control CRDT (Conflict-free Replicated Data Type) real-time collaborative editors POSIX

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A Concentration Bound for distributed Stochastic Approximation 58

A Concentration Bound for Distributed Stochastic Approximati...

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58th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

作者： Dolhare, Harsh Borkar, Vivek Indian Inst Technol Dept Elect Engn Mumbai Maharashtra India

ISBN: (数字)9798350399981

ISBN: (纸本)9798350399981

We revisit the classical model of Tsitsiklis, Bertsekas and Athans [10] for distributed stochastic approximation with consensus. The main result is an analysis of this scheme using the 'ODE' (for 'Ordinary Differential Equations') approach to stochastic approximation, leading to a high probability bound for the tracking error between suitably interpolated iterates and the limiting differential equation. Several future directions will also be highlighted.

关键词： distributed algorithms consensus two time scale algorithms ODE limit concentration bound

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A Multi-Stage Graph Aided Algorithm for distributed Service Function Chain Provisioning Across Multiple Domains

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IEEE ACCESS 2021年 9卷 114884-114904页

作者： Kibalya, Godfrey Serrat-Fernandez, Joan Gorricho, Juan-Luis Bujjingo, Doreen Gift Serugunda, Jonathan Univ Politecn Cataluna Dept Network Engn Barcelona 08034 Spain Makerere Univ Dept Elect & Comp Engn Kampala Uganda

Network Service Providers (NSPs) envisage to support the divergent and stringent requirements of future services by instantiating these services as service chains, commonly referred to as Service Function Chains (SFCs), that are customized and configured to meet specific service requirements. However, due to the limited footprint of the Infrastructure Providers (InPs), these SFCs may have to transcend multiple InPs/domains. In this regard, determining the optimal set of InPs in which to embed the SFC request emerges as a complex problem for several reasons. First, the large number of possible combinations for selecting the InPs to embed the different sub-chains of the request makes this problem computationally complex, rendering optimal solutions only after long computations, especially in large scale networks, which is unfeasible for delay sensitive applications. Second, the unwillingness of InPs to disclose their internal information, which may be vital for making embedding decisions, usually implies the provisioning of single-domain solutions, which are unsuitable in this working scenario. In this regard, this paper first formulates the multi-domain service deployment problem under multiple request constraints, such as bandwidth or delay, among others. Then, due to the NP-hardness nature of the above problem, this paper proposes an algorithm that is aided by a multi-stage graph for computing a request embedding solution in a distributed manner, solving the problem in acceptable run-times. Results from different simulations reveal that the proposed algorithm is optimized in terms of acceptance ratio and embedding cost, with up to 60.0% and 88.7% improvements in terms of embedding cost and execution time, respectively, for some scenarios, in comparison with a benchmark state-of-the-art algorithm.

关键词： Indium phosphide III-V semiconductor materials Delays Computer architecture distributed algorithms Service function chaining Licenses Service function chaining distributed algorithm multi-domain embedding network function virtualization

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Optimal Memory Requirement for Self-stabilizing Token Circulation 31st

Optimal Memory Requirement for Self-stabilizing Token Circul...

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31st International Colloquium on Structural Information and Communication Complexity (SIROCCO)

作者： Min, Lelia Le Bouder, Gabriel Petit, Franck Univ Paris Cite CNRS IRIF Paris France Univ Paris Saclay CNRS LMF Gif Sur Yvette France Sorbonne Univ CNRS LIP6 Paris France

ISBN: (纸本)9783031606021;9783031606038

In this paper, we consider networks where every transmitted message is received by all of the transmitter's neighbors. Typical such networks are wireless networks, in which to dedicate a message to a specific neighbor, the sender must specify who the recipient is by specifying the recipient's ID. Adding an identifier has a non-negligible cost, more precisely O(log n) bits in an n-node graph. Token Circulation (TC) is a fundamental problem that consists in guaranteeing that a single token circulates from one node to another, the token fairly visiting every node infinitely often. TC inherently requires that the token holder selects a unique neighboring node to which to pass the token. This paper proposes a solution that overcomes the communication of identifiers. It achieves optimal space complexity for the token circulation problem. The contribution of this paper is fourfold. First, we present Tok((sic)), the first deterministic depth-first token circulation algorithm for rooted wireless networks that uses only O(log log n) bits of memory per node. This is an exponential improvement compared to the classical addressing. Algorithm Tok((sic)) assumes a Destination-Oriented Directed Acyclic Graph (DODAG) spanning the network. Less popular than spanning trees, DODAGs are nonetheless more general and adaptable spanning structures, since they do not need to distinguish one neighboring node as unique parent. Second, Tok((sic)) has the very desirable property of being self-stabilizing. This means that starting from a configuration where zero or more than one token circulate in the network, the system is guaranteed to eventually work correctly, i.e., a single token eventually fairly visits every node infinitely often, following a depth-first order. Third, Tok((sic)) works under the unfair scheduler, that is the most challenging scheduling assumption of the model. Finally, we show that Tok((sic)) is optimal in terms of space complexity. Meaning that, for every n-node network,

关键词： distributed algorithms Self-Stabilization Token Circulation Memory Optimization

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A Fully Parallel distributed Algorithm for Non-Smooth Convex Optimization with Coupled Constraints: Application to Linear Algebraic Equations

A Fully Parallel Distributed Algorithm for Non-Smooth Convex...

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American Control Conference (ACC)

作者： Alaviani, S. Sh. Kelkar, A. G. Vaidya, U. Univ Georgia Sch Elect & Comp Engn Athens GA 30602 USA Clemson Univ Dept Mech Engn Clemson SC 29634 USA

ISBN: (数字)9781665451963

ISBN: (纸本)9781665451963

In this paper, collaborative optimization of sum of convex functions is considered where agents make decision using local information over networks subject to globally coupled affine equality and inequality constraints. In this problem, the globally coupled equality and inequality constraints' information is only partially accessible to each agent. The first discrete-time fully parallel distributed algorithm without diminishing step sizes, (sub)gradient, and/or solving a sub-problem at each time is derived based on monotone operator splitting approach. In the algorithm, the updates of variables happen independent of each other that results in reducing computational time per iteration significantly. The algorithm can converge to an optimal solution for any convex cost functions and any convex constraint sets of agents with arbitrary initialization over any undirected static (non-switching) networks in synchronous protocol. As an application of the problem, solving linear algebraic equations (LAEs) of the form Ax = b among m agents is considered where each agent only knows the partitioned matrix [A(i), b(i)] such that A = (Sigma(m)(i=1) A(i)) and b = (Sigma(m)(i=1) b(i)). The algorithm for LAEs is able to converge to an optimal solution for any matrices A and b.

关键词： Protocols Collaboration Cost function Convex functions Decision feedback equalizers Partitioning algorithms distributed algorithms

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