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randomized optimal consensus of multi-agent systems

AUTOMATICA 2012年第12期48卷 3018-3030页

作者： Shi, Guodong Johansson, Karl Henrik Royal Inst Technol KTH Sch Elect Engn ACCESS Linnaeus Ctr Automat Control Lab S-10044 Stockholm Sweden

In this paper, we formulate and solve a randomized optimal consensus problem for multi-agent systems with stochastically time-varying interconnection topology. The considered multi-agent system with a simple randomized iterating rule achieves an almost sure consensus meanwhile solving the optimization problem min(z is an element of Rd) Sigma(n)(i=1) f(i)(z), in which the optimal solution set of objective function f(i) can only be observed by agent i itself. At each time step, simply determined by a Bernoulli trial, each agent independently and randomly chooses either taking an average among its neighbor set, or projecting onto the optimal solution set of its own optimization component. Both directed and bidirectional communication graphs are studied. Connectivity conditions are proposed to guarantee an optimal consensus almost surely with proper convexity and intersection assumptions. The convergence analysis is carried out using convex analysis. We compare the randomized algorithm with the deterministic one via a numerical example. The results illustrate that a group of autonomous agents can reach an optimal opinion by each node simply making a randomized trade-off between following its neighbors or sticking to its own opinion at each time step. (c) 2012 Elsevier Ltd. All rights reserved.

关键词： Multi-agent systems Optimal consensus Set convergence Distributed optimization randomized algorithms

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randomized Iterative Methods for Matrix Approximation 1

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7th International Conference on Machine Learning, Optimization, and Data Science (LOD) / 1st Symposium on Artificial Intelligence and Neuroscience (ACAIN)

作者： Azzam, Joy Ong, Benjamin W. Struthers, Allan A. Michigan Technol Univ Dept Math Sci Houghton MI 49931 USA

ISBN: (数字)9783030954703

ISBN: (纸本)9783030954703;9783030954697

Standard tools to update approximations to a matrix A (for example, Quasi-Newton Hessian approximations in optimization) incorporate computationally expensive one-sided samples AV. This article develops randomized algorithms to efficiently approximate A by iteratively incorporating cheaper two-sided samples U-inverted perpendicular AV. Theoretical convergence rates are proved and realized in numerical experiments. A heuristic accelerated variant is developed and shown to be competitive with existing methods based on one-sided samples.

关键词： Matrix approximation randomized algorithms Two-sided samples Quasi-Newton

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randomized Computation for the Current Stress Policy Design in the DAB Converter

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IEEE CONTROL SYSTEMS LETTERS 2021年第3期5卷 863-868页

作者： Shen, Xun Ouyang, Tinghui Chen, Zhengxi Zhao, Shuang Fang, Jiaxin Zhang, Yahui Tokyo Univ Agr & Technol Dept Mech Syst Engn Tokyo 1848588 Japan Natl Inst Adv Ind Sci & Technol Artificial Intelligence Res Ctr Tokyo Bay Area Ctr Tokyo 1350064 Japan State Grid Corp China Global Energy Interconnect Grp Beijing 100031 Peoples R China Infineon Technol Amer Corp Automot Grp El Segundo CA 90245 USA Chinese Acad Sci Inst Software Beijing 100190 Peoples R China Sophia Univ Dept Engn & Appl Sci Tokyo 1028554 Japan

This letter addresses the current stress policy design in the Dual-Active-Bridge (DAB) converters with the randomized computation approach. First, a hybrid automaton approach is applied to model the dynamics of the DAB converter. Then the optimal feedback policy of a quadruple-phase-shift is obtained via solving a peak current minimization problem with DAB converter dynamics and transferred power constraints. A randomized optimization approach is applied to solve the problem. The proposed control scheme is validated by numerical simulation and compared with the traditional double-phase-shift and triple-phase-shift policies. The simulation results verify that the proposed quadruple-phase-shift method has better performance regarding the current stress.

关键词： randomized algorithms power electronics hybrid systems

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A randomized algorithm for two servers in cross polytope spaces

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THEORETICAL COMPUTER SCIENCE 2011年第7期412卷 563-572页

作者： Bein, Wolfgang Iwama, Kazuo Kawahara, Jun Larmore, Lawrence L. Oravec, James A. Univ Nevada Sch Comp Sci Ctr Adv Study Algorithms Las Vegas NV 89154 USA Kyoto Univ Sch Informat Kyoto 6068501 Japan

It has been a long-standing open problem to determine the exact randomized competitiveness of the 2-server problem, that is, the minimum competitiveness of any randomized online algorithm for the 2-server problem. For deterministic algorithms the best competitive ratio that can be obtained is 2 and no randomized algorithm is known that improves this ratio for general spaces. For the line, Bartal et al. (1998) [2] give a 155/78 competitive algorithm, but their algorithm is specific to the geometry of the line. We consider here the 2-server problem over Cross Polytope Spaces M-24. We obtain an algorithm with competitive ratio of and show that this ratio is best possible. This algorithm gives the second non-trivial example of metric spaces with better than 2-competitive ratio. The algorithm uses a design technique called the knowledge state technique a method not specific to M-24. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Online algorithms randomized algorithms Cross polytope spaces Server problem Algorithm design Algorithm engineering

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randomized methods bazed on new Monte Carlo schemes for convex optimization 20

Randomized methods bazed on new Monte Carlo schemes for conv...

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20th International Conference/Euro Mini Conference on Continuous Optimization and Knowledge-Based Technologies (EurOPT 2008)

作者： Polyak, Boris T. Gryazina, Elena N. RAS Inst Control Sci Moscow 117901 Russia

ISBN: (纸本)9789955282839

We address randomized methods for convex optimization based on generating points uniformly distributed in a convex set. We estimate the rate of convergence for such methods and demonstrate the link with the center of gravity method. To implement such approach we exploit two modem Monte Carlo schemes for generating points which are approximately uniformly distributed in a given convex set. Both methods use boundary oracle to find an intersection of a ray and the set. The first method is Hit-and-Run, the second is sometimes called Shake-and-Bake. Numerical simulation results look very promising

关键词： Monte Carlo optimization random search hit-and-run shake-and-bake randomized algorithms

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randomized data selection in detection with applications to distributed signal processing

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PROCEEDINGS OF THE IEEE 2003年第8期91卷 1184-1198页

作者： Sestok, CK Said, MR Oppenheim, AV MIT Elect Res Lab Cambridge MA 02139 USA

Performing robust detection with resource limitations such as low-power requirements or limited communication bandwidth is becoming increasingly important in contexts involving distributed signal processing. One way to address these constraints consists of reducing the amount of data used by the detection algorithms. Intelligent data selection in detection can be highly dependent on a priori information about the signal and noise. In this paper we explore detection strategies based on randomized data selection and analyze the resulting algorithms' performance. randomized data selection is a viable approach in the absence of reliable and detailed a priori information, and it provides a reasonable lower bound on signal processing performance as more a priori information is incorporated. The randomized selection procedure has the added benefits of simple implementation in a distributed environment and limited communication overhead. As an example of detection algorithms based upon randomized selection, we analyze a binary hypothesis testing problem, and determine several useful properties of detectors derived from the likelihood ratio test. Additionally, we suggest an adaptive detector that accounts for fluctuations in the selected data subset. The advantages and disadvantages of this approach in distributed sensor networks applications are also discussed.

关键词： distributed signal processing likelihood ratio test nonparametric detection randomized algorithms randomized sampling sensor networks

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randomized sampling for large zero-sum games

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AUTOMATICA 2013年第5期49卷 1184-1194页

作者： Bopardikar, Shaunak D. Borri, Alessandro Hespanha, Joao P. Prandini, Maria Di Benedetto, Maria D. United Technol Res Ctr Inc Embedded Syst & Networks Grp Berkeley CA USA Consiglio Nazl Ric IASI CNR Ist Anal Sistemi & Informat A Ruberti Rome Italy Univ Calif Santa Barbara Ctr Control Dynam Syst & Computat Santa Barbara CA 93106 USA Politecn Milan Dipartimento Elettron Informaz & Bioingn Milan Italy Univ Aquila Dept Elect & Informat Engn I-67100 Laquila Italy Univ Calif Santa Barbara Santa Barbara CA 93106 USA

This paper addresses the solution of large zero-sum matrix games using randomized methods. We formalize a procedure, termed as the sampled security policy (SSP) algorithm, by which a player can compute policies that, with a high confidence, are security policies against an adversary using randomized methods to explore the possible outcomes of the game. The SSP algorithm essentially consists of solving a stochastically sampled subgame that is much smaller than the original game. We also propose a randomized algorithm, termed as the sampled security value (SSV) algorithm, which computes a high-confidence security-level (i.e., worst-case outcome) for a given policy, which may or may not have been obtained using the SSP algorithm. For both the SSP and the SSV algorithms we provide results to determine how many samples are needed to guarantee a desired level of confidence. We start by providing results when the two players sample policies with the same distribution and subsequently extend these results to the case of mismatched distributions. We demonstrate the usefulness of these results in a hide-and-seek game that exhibits exponential complexity. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Game theory randomized algorithms Zero-sum games Optimization

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Measuring the Algorithmic Convergence of randomized Ensembles: The Regression Setting

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SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE 2020年第4期2卷 921-943页

作者： Lopes, Miles E. Wu, Suofei Lee, Thomas C. M. Univ Calif Davis Dept Stat Davis CA 95616 USA

When randomized ensemble methods such as bagging and random forests are implemented, a basic question arises: Is the ensemble large enough? In particular, the practitioner desires a rigorous guarantee that a given ensemble will perform nearly as well as an ideal infinite ensemble (trained on the same data). The purpose of the current paper is to develop a bootstrap method for solving this problem in the context of regression-which complements our companion paper in the context of classification [Lopes, Ann. Statist., 47 (2019), 1088-1112]. In contrast to the classification setting, the current paper shows that theoretical guarantees for the proposed bootstrap can be established under much weaker assumptions. In addition, we illustrate the flexibility of the method by showing how it can be adapted to measure algorithmic convergence for variable selection. Lastly, we provide numerical results demonstrating that the method works well in a range of situations.

关键词： bagging bootstrap randomized algorithms random forests

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A simple randomized k-local election algorithm for local computations

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4th International Workshop on Experimental and Efficient algorithms

作者： Ossamy, R Univ Bordeaux 1 LaBRI F-33405 Talence France

ISBN: (纸本)3540259201

Most of distributed algorithms encoded by means of local computations [3] need to solve k-local election problems to ensure a faithful relabeling of disjoint subgraphs. Due to a result stated in [1], it is not possible to solve the k-local election problem for k >= 3 in anonymous networks. Based on distributed computations of rooted trees of minimal paths, we present in this paper a simple randomized algorithm which, with very high probability, solves the k-local election problem (k >= 2) in an anonymous graph.

关键词： local computations election in graphs distributed algorithms randomized algorithms

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Non-independent randomized rounding and coloring

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DISCRETE APPLIED MATHEMATICS 2006年第4期154卷 650-659页

作者： Doerr, B Univ Kiel Math Seminar D-24098 Kiel Germany

We propose an advanced randomized coloring algorithm for the problem of balanced colorings of hypergraphs (discrepancy problem). Instead of independently coloring the vertices with a random color, we try to use structural information about the hypergraph in the design of the random experiment by imposing suitable dependencies. This yields colorings having smaller discrepancy. We also obtain more information about the coloring, or, conversely, we may enforce the random coloring to have special properties. There are some algorithmic advantages as well. We apply our approach to hypergraphs of d-dimensional boxes and to finite geometries. Among others results, we gain a factor 2(d/2) decrease in the discrepancy of the boxes, and reduce the number of random bits needed to generate good colorings for the geometries down to O(root n) (from n). The latter also speeds up the corresponding derandomization by a factor of root n. (c) 2005 Elsevier B.V. All rights reserved.

关键词： randomized algorithms hypergraph coloring discrepancy randomized rounding integer linear programming

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