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A UNIFIED FRAMEWORK FOR CONTINUOUS-TIME UNCONSTRAINED DISTRIBUTED OPTIMIZATION

SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2023年第4期61卷 2004-2020页

作者： Touri, Behrouz Gharesifard, Bahman Univ Calif San Diego Dept Elect & Comp La Jolla CA 92093 USA Univ Calif Los Angeles Dept Elect & Comp Engn Los Angeles CA 90095 USA

We introduce a class of distributed nonlinear control systems, termed as the flow-tracker dynamics, which capture phenomena where the average state is controlled by the average control input, with no individual agent having direct access to this average. The agents update their estimates of the average through a nonlinear observer. We prove that utilizing a proper gradient feedback for any distributed control system that satisfies these conditions will lead to a solution of the corresponding distributed optimization problem. We show that many of the existing algorithms for solving distributed optimization are instances of this dynamics, and hence their convergence properties can follow from its properties. In this sense, the proposed method establishes a unified framework for distributed optimization in continuous time. Moreover, this formulation allows us to introduce a suit of new continuous-time distributed optimization algorithms by readily extending the graph-theoretic conditions under which such dynamics are convergent.

关键词： distributed optimization distributed control push-sum algorithm saddle-point dynamics averaging dynamics

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push-sum Distributed Online Optimization With Bandit Feedback

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IEEE TRANSACTIONS ON CYBERNETICS 2022年第4期52卷 2263-2273页

作者： Wang, Cong Xu, Shengyuan Yuan, Deming Zhang, Baoyong Zhang, Zhengqiang Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Peoples R China Qufu Normal Univ Sch Elect Engn & Automat Rizhao 276826 Peoples R China

In this article, we concentrate on distributed online convex optimization problems over multiagent systems, where the communication between nodes is represented by a class of directed graphs that are time varying and uniformly strongly connected. This problem is in bandit feedback, in the sense that at each time only the cost function value at the committed point is revealed to each node. Then, nodes update their decisions by exchanging information with their neighbors only. To deal with Lipschitz continuous and strongly convex cost functions, a distributed online convex optimization algorithm that achieves sublinear individual regret for every node is developed. The algorithm is built on the algorithm called the push-sum scheme that releases the request of doubly stochastic weight matrices, and the one-point gradient estimator that requires the function value at only one point at every iteration, instead of the gradient information of loss function. The expected regret of our proposed algorithm scales as O(T-2/3 ln(2/3)(T)), and T is the number of iterations. To validate the performance of the algorithm developed in this article, we give a simulation of a common numerical example.

关键词： Distributed online optimization multiagent systems one-point bandit feedback push-sum algorithm

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Online Expectation-Maximization Based Frequency and Phase Consensus in Distributed Phased Arrays

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IEEE TRANSACTIONS ON COMMUNICATIONS 2023年第6期71卷 3721-3735页

作者： Rashid, Mohammed Nanzer, Jeffrey A. Michigan State Univ Elect & Comp Engn Dept E Lansing MI 48824 USA

A distributed phased array is comprised of separate, smaller antenna systems (nodes) that coordinate with each other to support coherent beamforming. However, due to the frequency drift and phase jitter of the oscillators on the nodes, as well as the frequency and phase estimation errors induced in the synchronization process, there exists a decoherence between the nodes that degrades their beamforming gain. A decentralized frequency and phase consensus (DFPC) algorithm was proposed in a prior work for undirected array networks in which the nodes locally share their frequencies and phases with their neighboring nodes to reach a synchronized state. Kalman filtering (KF) was also integrated with DFPC, and the resulting KF-DFPC showed significant reduction in the total residual phase error upon convergence. One limitation of the DFPC-based algorithms is that, due to relying on the average consensus protocol which assumes undirected networks, they do not generally converge for directed array networks with column stochastic weighting matrix. For directed networks, a push-sum protocol based frequency alignment algorithm was recently proposed, but it does not take into account both frequency and phase variations in-between the update intervals. In this paper, we model the variations using a first-order Markov process and propose a push-sum based frequency and phase consensus (PsFPC) algorithm which is accordingly a modified version of the push-sum protocol. The residual phase error of PsFPC upon convergence is theoretically derived as well. Kalman filtering is also integrated with PsFPC and the resulting KF-PsFPC algorithm shows significant reduction in the residual error of the array. A limitation of KF-PsFPC is that the model parameters, i.e., the measurement noise and the process noise covariance matrices, are assumed to be known a priori. Since they may not be known in practice, we develop an online expectation maximization (EM) based algorithm that iteratively compute

关键词： Distributed beamforming distributed phased arrays frequency and phase consensus Kalman filtering online expectation maximization push-sum algorithm

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Dynamic Average Diffusion With Randomized Coordinate Updates

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IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS 2019年第4期5卷 753-767页

作者： Ying, Bicheng Yuan, Kun Sayed, Ali H. Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90095 USA Ecole Polytech Fed Lausanne Sch Engn CH-1015 Lausanne Switzerland

This work derives and analyzes an online learning strategy for tracking the average of time-varying distributed signals by relying on randomized coordinate-descent updates. During each iteration, each agent selects or observes a random entry of the observation vector, and different agents may select different entries of their observations before engaging in a consultation step. Careful coordination of the interactions among agents is necessary to avoid bias and ensure convergence. We provide a convergence analysis for the proposed methods, and illustrate the results by means of simulations.

关键词： Heuristic algorithms Indexes Convergence Optimization Information processing Distributed algorithms Network topology Dynamic average diffusion consensus push-sum algorithm coordinate descent exact diffusion

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push-sum Protocol Based Frequency and Phase Synchronization in Distributed Phased Arrays

Push-Sum Protocol Based Frequency and Phase Synchronization ...

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IEEE International Symposium on Phased Array Systems and Technology (PAST)

作者： Rashid, Mohammed Nanzer, Jeffrey A.

ISBN: (数字)9781665441667

ISBN: (纸本)9781665441667

In this paper, we consider the problem of joint frequency and phase synchronization of the nodes in a distributed phased array, when the communication links between the nodes are unidirectional. We assume a signal model for each node wherein oscillator frequency and phase drifts and phase jitter are included. Furthermore, we suppose that the nodes iteratively share their updated frequencies and phases via a local broadcast of their signals to reach a consensus, and thus the estimation errors are also included in the signal model. A push-sum protocol based frequency and phase consensus (PsFPC) algorithm is proposed for the array synchronization. Simulation results are included where it is shown that the performance of PsFPC improves with an increase in the number of nodes in the array, the connectivity between the nodes, and the signal to noise ratio of the received signals.

关键词： Distributed beamforming distributed phased arrays frequency and phase consensus oscillator frequency drift and phase noise push-sum algorithm

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Improving Fault Tolerance and Accuracy of a Distributed Reduction algorithm

Improving Fault Tolerance and Accuracy of a Distributed Redu...

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25th ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis (SC)

作者： Niederbrucker, Gerhard Strakova, Hana Gansterer, Wilfried N. Univ Vienna Res Grp Theory & Applicat Algorithms A-1010 Vienna Austria

ISBN: (纸本)9780769549569;9781467362184

Most existing algorithms for parallel or distributed reduction operations are not able to handle temporary or permanent link and node failures. Only recently, methods were proposed which are in principal capable of tolerating link and node failures as well as soft errors like bit flips or message loss. A particularly interesting example is the push-flow algorithm. However, on closer inspection, it turns out that in this method the failure recovery often implies severe performance drawbacks. Existing mechanisms for failure handling may basically lead to a fall-back to an early stage of the computation and consequently slow down convergence or even prevent convergence if failures occur too frequently. Moreover, state-of-the-art fault tolerant distributed reduction algorithms may experience accuracy problems even in failure free systems. We present the push-cancel-flow (PCF) algorithm, a novel algorithmic enhancement of the push-flow algorithm. We show that the new push-cancel-flow algorithm exhibits superior accuracy, performance and fault tolerance over all other existing distributed reduction methods. Moreover, we employ the novel PCF algorithm in the context of a fully distributed QR factorization process and illustrate that the improvements achieved at the reduction level directly translate to higher level matrix operations, such as the considered QR factorization.

关键词： push-cancel-flow algorithm push-flow algorithm push-sum algorithm

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A Distributed Eigensolver for Loosely Coupled Networks

A Distributed Eigensolver for Loosely Coupled Networks

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21st Euromicro International Conference on Parallel, Distributed, and Network-Based Processing (PDP)

作者： Strakova, Hana Gansterer, Wilfried N. Univ Vienna Res Grp Theory & Applicat Algorithms Vienna Austria

ISBN: (纸本)9780769549392;9781467353212

We introduce a new distributed eigensolver (dOI) for square matrices based on orthogonal iteration. In contrast to standard parallel eigensolvers, our approach performs only nearest neighbor communication and provides much more flexibility with respect to the properties of the hardware infrastructure on which the computation is performed. This is achieved by utilizing distributed summation methods with randomized communication schedules which do not require global synchronization across the nodes. Our algorithm is particularly attractive for loosely coupled distributed networks with arbitrary network topologies and potentially unreliable components. Our distributed eigensolver dOI is based on a novel distributed matrix-matrix multiplication algorithm and on an extension of a distributed QR factorization algorithm proposed earlier. We illustrate the advantages of dOI in terms of higher flexibility with respect to the underlying network and lower communication cost compared to a related distributed eigensolver by Kempe and McSherry. Moreover, we experimentally illustrate how the overall communication cost of dOI is further reduced by adapting the accuracy of each distributed summation during the orthogonal iteration process.

关键词： distributed eigensolver distributed orthogonal iteration gossip-based algorithm push-sum algorithm randomized communication schedule

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