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  1. Book ; Online: On Lyapunov functions for open Hegselmann-Krause dynamics

    Vizuete, Renato / Frasca, Paolo / Panteley, Elena

    2023  

    Abstract: In this paper, we provide a formulation of an open Hegselmann-Krause (HK) dynamics where agents can join and leave the system during the interactions. We consider a stochastic framework where the time instants corresponding to arrivals and departures are ...

    Abstract In this paper, we provide a formulation of an open Hegselmann-Krause (HK) dynamics where agents can join and leave the system during the interactions. We consider a stochastic framework where the time instants corresponding to arrivals and departures are determined by homogeneous Poisson processes. Then, we provide a survey of Lyapunov functions based on global and local disagreement, whose asymptotic behavior can be used to measure the impact of arrivals and departures. After proving analytical results on these Lyapunov functions in the open system, we illustrate them through numerical simulations in two scenarios characterized by a different number of expected agents.

    Comment: 17 pages, 2 figures
    Keywords Electrical Engineering and Systems Science - Systems and Control ; Computer Science - Social and Information Networks ; Mathematics - Optimization and Control
    Publishing date 2023-03-13
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  2. Book ; Online: On the Influence of Noise in Randomized Consensus Algorithms

    Vizuete, Renato / Frasca, Paolo / Panteley, Elena

    2020  

    Abstract: In this paper we study the influence of additive noise in randomized consensus algorithms. Assuming that the update matrices are symmetric, we derive a closed form expression for the mean square error induced by the noise, together with upper and lower ... ...

    Abstract In this paper we study the influence of additive noise in randomized consensus algorithms. Assuming that the update matrices are symmetric, we derive a closed form expression for the mean square error induced by the noise, together with upper and lower bounds that are simpler to evaluate. Motivated by the study of Open Multi-Agent Systems, we concentrate on Randomly Induced Discretized Laplacians, a family of update matrices that are generated by sampling subgraphs of a large undirected graph. For these matrices, we express the bounds by using the eigenvalues of the Laplacian matrix of the underlying graph or the graph's average effective resistance, thereby proving their tightness. Finally, we derive expressions for the bounds on some examples of graphs and numerically evaluate them.

    Comment: 6 pages, submitted to IEEE Control Systems Letters
    Keywords Electrical Engineering and Systems Science - Systems and Control ; Mathematics - Optimization and Control
    Subject code 510
    Publishing date 2020-06-10
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  3. Book ; Online: The Laplacian Spectrum of Large Graphs Sampled from Graphons

    Vizuete, Renato / Garin, Federica / Frasca, Paolo

    2020  

    Abstract: This paper studies the Laplacian spectrum and the average effective resistance of (large) graphs that are sampled from graphons. Broadly speaking, our main finding is that the Laplacian eigenvalues of a large dense graph can be effectively approximated ... ...

    Abstract This paper studies the Laplacian spectrum and the average effective resistance of (large) graphs that are sampled from graphons. Broadly speaking, our main finding is that the Laplacian eigenvalues of a large dense graph can be effectively approximated by using the degree function of the corresponding graphon. More specifically, we show how to approximate the distribution of the Laplacian eigenvalues and the average effective resistance (Kirchhoff index) of the graph. For all cases, we provide explicit bounds on the approximation errors and derive the asymptotic rates at which the errors go to zero when the number of nodes goes to infinity. Our main results are proved under the conditions that the graphon is piecewise Lipschitz and bounded away from zero.

    Comment: 10 pages, 6 figures, submitted on April 20, 2020
    Keywords Mathematics - Probability ; Electrical Engineering and Systems Science - Systems and Control ; Mathematics - Optimization and Control
    Subject code 519
    Publishing date 2020-04-20
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  4. Book ; Online: Random Coordinate Descent for Resource Allocation in Open Multi-Agent Systems

    de Galland, Charles Monnoyer / Vizuete, Renato / Hendrickx, Julien M. / Panteley, Elena / Frasca, Paolo

    2022  

    Abstract: We analyze the distributed random coordinate descent algorithm for solving separable resource allocation problems in the context of an open multi-agent system, where agents can be replaced during the process. First, we establish the linear convergence of ...

    Abstract We analyze the distributed random coordinate descent algorithm for solving separable resource allocation problems in the context of an open multi-agent system, where agents can be replaced during the process. First, we establish the linear convergence of the algorithm in closed systems, in terms of the estimate towards the minimizer, for general graphs and appropriate step-size. Next, we estimate the change of the optimal solution after a replacement to evaluate its effect on the distance between the estimate and the minimizer. From these two elements, we derive stability conditions in open systems and establish the linear convergence of the algorithm towards a steady state expected error. Our results allow characterizing the trade-off between speed of convergence and robustness to agent replacements, under the assumptions that local functions are smooth strongly convex and have their minimizers located in a given ball.

    Comment: 13 pages, 9 figures, submitted to IEEE Transactions on Automatic Control
    Keywords Computer Science - Multiagent Systems ; Mathematics - Optimization and Control
    Subject code 510
    Publishing date 2022-05-20
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  5. Book ; Online: Resource allocation in open multi-agent systems

    Vizuete, Renato / de Galland, Charles Monnoyer / Hendrickx, Julien M. / Frasca, Paolo / Panteley, Elena

    an online optimization analysis

    2022  

    Abstract: The resource allocation problem consists of the optimal distribution of a budget between agents in a group. We consider such a problem in the context of open systems, where agents can be replaced at some time instances. These replacements lead to ... ...

    Abstract The resource allocation problem consists of the optimal distribution of a budget between agents in a group. We consider such a problem in the context of open systems, where agents can be replaced at some time instances. These replacements lead to variations in both the budget and the total cost function that hinder the overall network's performance. For a simple setting, we analyze the performance of the Random Coordinate Descent algorithm (RCD) using tools similar to those commonly used in online optimization. In particular, we study the accumulated errors that compare solutions issued from the RCD algorithm and the optimal solution or the non-collaborating selfish strategy and we derive some bounds in expectation for these accumulated errors.

    Comment: 7 pages, 3 figures, accepted for the 61st Conference on Decision and Control (CDC2022)
    Keywords Computer Science - Multiagent Systems ; Mathematics - Optimization and Control
    Subject code 510
    Publishing date 2022-07-19
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  6. Book ; Online: Random coordinate descent algorithm for open multi-agent systems with complete topology and homogeneous agents

    de Galland, Charles Monnoyer / Vizuete, Renato / Hendrickx, Julien M. / Frasca, Paolo / Panteley, Elena

    2021  

    Abstract: We study the convergence in expectation of the Random Coordinate Descent algorithm (RCD) for solving optimal resource allocations problems in open multi-agent systems, i.e., multi-agent systems that are subject to arrivals and departures of agents. ... ...

    Abstract We study the convergence in expectation of the Random Coordinate Descent algorithm (RCD) for solving optimal resource allocations problems in open multi-agent systems, i.e., multi-agent systems that are subject to arrivals and departures of agents. Assuming all local functions are strongly-convex and smooth, and their minimizers lie in a given ball, we analyse the evolution of the distance to the minimizer in expectation when the system is occasionally subject to replacements in addition to the usual iterations of the RCD algorithm. We focus on complete graphs where all agents interact with each other with the same probability, and provide conditions to guarantee convergence in open system. Finally, a discussion around the tightness of our results is provided.

    Comment: 8 pages, 3 figures, to be published in proceedings of the 60th IEEE Conference on Decision and Control (CDC2021)
    Keywords Computer Science - Multiagent Systems ; Mathematics - Optimization and Control
    Subject code 006
    Publishing date 2021-09-29
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

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