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  1. Article ; Online: Efficient Algorithm for Approximating Nash Equilibrium of Distributed Aggregative Games.

    Xu, Gehui / Chen, Guanpu / Qi, Hongsheng / Hong, Yiguang

    IEEE transactions on cybernetics

    2023  Volume 53, Issue 7, Page(s) 4375–4387

    Abstract: In this article, we aim to design a distributed approximate algorithm for seeking Nash equilibria (NE) of an aggregative game. Due to the local set constraints of each player, projection-based algorithms have been widely employed for solving such ... ...

    Abstract In this article, we aim to design a distributed approximate algorithm for seeking Nash equilibria (NE) of an aggregative game. Due to the local set constraints of each player, projection-based algorithms have been widely employed for solving such problems actually. Since it may be quite hard to get the exact projection in practice, we utilize inscribed polyhedrons to approximate local set constraints, which yields a related approximate game model. We first prove that the NE of the approximate game is the ϵ -NE of the original game and then propose a distributed algorithm to seek the ϵ -NE, where the projection is then of a standard form in quadratic optimization with linear constraints. With the help of the existing developed methods for solving quadratic optimization, we show the convergence of the proposed algorithm and also discuss the computational cost issue related to the approximation. Furthermore, based on the exponential convergence of the algorithm, we estimate the approximation accuracy related to ϵ . In addition, we investigate the computational cost saved by approximation in numerical simulation.
    MeSH term(s) Algorithms ; Computer Simulation
    Language English
    Publishing date 2023-06-15
    Publishing country United States
    Document type Journal Article
    ISSN 2168-2275
    ISSN (online) 2168-2275
    DOI 10.1109/TCYB.2022.3175831
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article ; Online: Projective Incomplete Multi-View Clustering.

    Deng, Shijie / Wen, Jie / Liu, Chengliang / Yan, Ke / Xu, Gehui / Xu, Yong

    IEEE transactions on neural networks and learning systems

    2023  Volume PP

    Abstract: Due to the rapid development of multimedia technology and sensor technology, multi-view clustering (MVC) has become a research hotspot in machine learning, data mining, and other fields and has been developed significantly in the past decades. Compared ... ...

    Abstract Due to the rapid development of multimedia technology and sensor technology, multi-view clustering (MVC) has become a research hotspot in machine learning, data mining, and other fields and has been developed significantly in the past decades. Compared with single-view clustering, MVC improves clustering performance by exploiting complementary and consistent information among different views. Such methods are all based on the assumption of complete views, which means that all the views of all the samples exist. It limits the application of MVC, because there are always missing views in practical situations. In recent years, many methods have been proposed to solve the incomplete MVC (IMVC) problem and a kind of popular method is based on matrix factorization (MF). However, such methods generally cannot deal with new samples and do not take into account the imbalance of information between different views. To address these two issues, we propose a new IMVC method, in which a novel and simple graph regularized projective consensus representation learning model is formulated for incomplete multi-view data clustering task. Compared with the existing methods, our method not only can obtain a set of projections to handle new samples but also can explore information of multiple views in a balanced way by learning the consensus representation in a unified low-dimensional subspace. In addition, a graph constraint is imposed on the consensus representation to mine the structural information inside the data. Experimental results on four datasets show that our method successfully accomplishes the IMVC task and obtain the best clustering performance most of the time. Our implementation is available at https://github.com/Dshijie/PIMVC.
    Language English
    Publishing date 2023-02-10
    Publishing country United States
    Document type Journal Article
    ISSN 2162-2388
    ISSN (online) 2162-2388
    DOI 10.1109/TNNLS.2023.3242473
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  3. Book ; Online: Global solution to sensor network localization

    Xu, Gehui / Chen, Guanpu / Hong, Yiguang / Fidan, Baris / Parisini, Thomas / Johansson, Karl H.

    A non-convex potential game approach and its distributed implementation

    2024  

    Abstract: Consider a sensor network consisting of both anchor and non-anchor nodes. We address the following sensor network localization (SNL) problem: given the physical locations of anchor nodes and relative measurements among all nodes, determine the locations ... ...

    Abstract Consider a sensor network consisting of both anchor and non-anchor nodes. We address the following sensor network localization (SNL) problem: given the physical locations of anchor nodes and relative measurements among all nodes, determine the locations of all non-anchor nodes. The solution to the SNL problem is challenging due to its inherent non-convexity. In this paper, the problem takes on the form of a multi-player non-convex potential game in which canonical duality theory is used to define a complementary dual potential function. After showing the Nash equilibrium (NE) correspondent to the SNL solution, we provide a necessary and sufficient condition for a stationary point to coincide with the NE. An algorithm is proposed to reach the NE and shown to have convergence rate $\mathcal{O}(1/\sqrt{k})$. With the aim of reducing the information exchange within a network, a distributed algorithm for NE seeking is implemented and its global convergence analysis is provided. Extensive simulations show the validity and effectiveness of the proposed approach to solve the SNL problem.

    Comment: arXiv admin note: text overlap with arXiv:2311.03326
    Keywords Mathematics - Optimization and Control ; Computer Science - Computer Science and Game Theory ; Computer Science - Multiagent Systems
    Subject code 000
    Publishing date 2024-01-04
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Book ; Online: Coincidence analysis of Stackelberg and Nash equilibria in three-player leader-follower security games

    Xu, Gehui / Chen, Guanpu / Cheng, Zhaoyang / Hong, Yiguang / Qi, Hongsheng

    2022  

    Abstract: There has been significant recent interest in leader-follower security games, where the leader dominates the decision process with the Stackelberg equilibrium (SE) strategy. However, such a leader-follower scheme may become invalid in practice due to ... ...

    Abstract There has been significant recent interest in leader-follower security games, where the leader dominates the decision process with the Stackelberg equilibrium (SE) strategy. However, such a leader-follower scheme may become invalid in practice due to subjective or objective factors, and then the Nash equilibrium (NE) strategy may be an alternative option. In this case, the leader may face a dilemma of choosing an SE strategy or an NE strategy. In this paper, we focus on a unified three-player leader-follower security game and study the coincidence between SE and NE. We first explore a necessary and sufficient condition for the case that each SE is an NE, which can be further presented concisely when the SE is unique. This condition not only provides access to seek a satisfactory SE strategy but also makes a criterion to verify an obtained SE strategy. Then we provide another appropriate condition for the case that at least one SE is an NE. Moreover, since the coincidence condition may not always be satisfied, we describe the closeness between SE and NE, and give an upper bound of their deviation. Finally, we show the applicability of the obtained theoretical results in several practical security cases, including the secure transmission problem and the cybersecurity defense.
    Keywords Computer Science - Computer Science and Game Theory ; Mathematics - Optimization and Control
    Publishing date 2022-10-28
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Book ; Online: Global Nash Equilibrium in Non-convex Multi-player Game

    Chen, Guanpu / Xu, Gehui / He, Fengxiang / Hong, Yiguang / Rutkowski, Leszek / Tao, Dacheng

    Theory and Algorithms

    2023  

    Abstract: Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the non-convexity, ... ...

    Abstract Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the non-convexity, obtaining the existence condition of global NE is challenging, let alone designing theoretically guaranteed realization algorithms. This paper takes conjugate transformation to the formulation of non-convex multi-player games, and casts the complementary problem into a variational inequality (VI) problem with a continuous pseudo-gradient mapping. We then prove the existence condition of global NE: the solution to the VI problem satisfies a duality relation. Based on this VI formulation, we design a conjugate-based ordinary differential equation (ODE) to approach global NE, which is proved to have an exponential convergence rate. To make the dynamics more implementable, we further derive a discretized algorithm. We apply our algorithm to two typical scenarios: multi-player generalized monotone game and multi-player potential game. In the two settings, we prove that the step-size setting is required to be $\mathcal{O}(1/k)$ and $\mathcal{O}(1/\sqrt k)$ to yield the convergence rates of $\mathcal{O}(1/ k)$ and $\mathcal{O}(1/\sqrt k)$, respectively. Extensive experiments in robust neural network training and sensor localization are in full agreement with our theory.
    Keywords Computer Science - Computer Science and Game Theory ; Computer Science - Machine Learning ; Mathematics - Optimization and Control ; Statistics - Machine Learning
    Publishing date 2023-01-19
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  6. Book ; Online: Non-convex potential game approach to global solution in sensor network localization

    Xu, Gehui / Chen, Guanpu / Hong, Yiguang / Parisini, Thomas / Fidan, Baris / Johansson, Karl H.

    2023  

    Abstract: Sensor network localization (SNL) problems require determining the physical coordinates of all sensors in a network. This process relies on the global coordinates of anchors and the available measurements between non-anchor and anchor nodes. Attributed ... ...

    Abstract Sensor network localization (SNL) problems require determining the physical coordinates of all sensors in a network. This process relies on the global coordinates of anchors and the available measurements between non-anchor and anchor nodes. Attributed to the intrinsic non-convexity, obtaining a globally optimal solution to SNL is challenging, as well as implementing corresponding algorithms. In this paper, we formulate a non-convex multi-player potential game for a generic SNL problem to investigate the identification condition of the global Nash equilibrium (NE) therein, where the global NE represents the global solution of SNL. We employ canonical duality theory to transform the non-convex game into a complementary dual problem. Then we develop a conjugation-based algorithm to compute the stationary points of the complementary dual problem. On this basis, we show an identification condition of the global NE: the stationary point of the proposed algorithm satisfies a duality relation. Finally, simulation results are provided to validate the effectiveness of the theoretical results.
    Keywords Mathematics - Optimization and Control ; Computer Science - Computer Science and Game Theory ; Computer Science - Multiagent Systems
    Subject code 006
    Publishing date 2023-11-06
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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