作者：
Xinxiang GuoYifen MuXiaoguang YangSchool of Mathematical Sciences
University of Chinese Academy of Sciences and The Key Laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China The Key Laboratory of Systems and Control
Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China The Key Laboratory of Management
Decision and Information System Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China
In this paper, we consider the $n \times n$ two-payer zero-sum repeated game in which one player (player X) employs the popular Hedge (also called multiplicative weights update) learning algorithm while the other play...
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ISBN:
(数字)9798350316339
ISBN:
(纸本)9798350316346
In this paper, we consider the $n \times n$ two-payer zero-sum repeated game in which one player (player X) employs the popular Hedge (also called multiplicative weights update) learning algorithm while the other player (player Y) adopts the myopic best response. The theoretical analysis on the dynamics of such game system is still rare, which is however of promising interests. We investigate the dynamics of such Hedge-myopic system by defining a metric $Q\left(\mathbf{x}_{t}\right)$, which measures the distance between the stage strategy x t and Nash Equilibrium (NE) strategy of player $\mathbf{X}$. We analyze the trend of $Q\left(\mathbf{x}_{t}\right)$ and prove that it is bounded and can only take finite values on the evolutionary path when payoffs are all rational numbers and the game has an interior NE. Based on this, we prove that the stage strategy sequence of both players are periodic after finite stages and the time-averaged strategy of player Y within one period is an exact NE strategy.
With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and ***,there has been little theoretical work focusing o...
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With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and ***,there has been little theoretical work focusing on neural networks in solving interface *** this paper,we perform a convergence analysis of physics-informed neural networks(PINNs)for solving second-order elliptic interface ***,we consider PINNs with domain decomposition technologies and introduce gradient-enhanced strategies on the interfaces to deal with boundary and interface jump *** is shown that the neural network sequence obtained by minimizing a Lipschitz regularized loss function converges to the unique solution to the interface problem in H2 as the number of samples *** experiments are provided to demonstrate our theoretical analysis.
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates...
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Laplacian dynamics on signed digraphs have a richer behavior than those on nonnegative digraphs. In particular, for the so-called 'repelling' signed Laplacians, the marginal stability property (needed to achie...
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First of all, I would like to take this opportunity to express my sincere and deep thanks to our Editor-in-Chief, Professor Meng Chu Zhou, who took over my position after I was drafted for rejuvenating IEEE Transactio...
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First of all, I would like to take this opportunity to express my sincere and deep thanks to our Editor-in-Chief, Professor Meng Chu Zhou, who took over my position after I was drafted for rejuvenating IEEE Transactions on Computational Social systems in 2017. During the past five years, Meng Chu’s professional leadership and dedication has transformed IEEE/CAA Journal of Automatica Sinica(JAS) from its infancy to a young and high-impact publication in the world that is full of vitality and actively engaged by a group of talented and charged associate Ei Cs and editors, which is clearly demonstrated in Meng Chu’s farewell editorial [1]. I am very glad that Professor Qing-Long Han, an influential and leading scientist of the world-class in AI, control, automation, and intelligent science and technology from Australia, as well as a staunch supporter and great leader of this journal from its beginning, will take over the Ei C torch from Meng Chu next year, since I am extremely confident that our journal will reach a new high for its service and quality under his new leadership.
The semi-tensor product (STP) of matrices is extended to the STP of hypermatrices. Some basic properties of the STP of matrices are extended to the STP of hypermatrices. The hyperdeterminant of hypersquares is introdu...
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Tensor networks have been a powerful tool in simulating many-body physics and have recently gained recognition in the machine learning community due to their remarkable representation capabilities. However, using tens...
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Tensor networks have been a powerful tool in simulating many-body physics and have recently gained recognition in the machine learning community due to their remarkable representation capabilities. However, using tensor networks to address the problem of clustering with an indeterminate number of clusters has yet to be explored.
The semi-tensor product (STP) approach to logical reasoning is proposed. After reviewing the notions of formal reasoning for propositions, we show how mathematical reasoning for propositions can be verified using the ...
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For a convex,coercive continuous Hamiltonian on a closed Riemannian manifold M,we construct a unique forward weak KAM solution of H(x,d_(x)u)=c(H)by a vanishing discount approach,where c(H)is the Ma?écritical ***...
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For a convex,coercive continuous Hamiltonian on a closed Riemannian manifold M,we construct a unique forward weak KAM solution of H(x,d_(x)u)=c(H)by a vanishing discount approach,where c(H)is the Ma?écritical *** also discuss the dynamical significance of such a special solution.
Let Mn be an embedded closed submanifold ofR^(k+1) or a smooth bounded domain inR_(n),where n≥*** show that the local smooth solution to the heat flow of self-induced harmonic map will blow up at a finite time,provid...
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Let Mn be an embedded closed submanifold ofR^(k+1) or a smooth bounded domain inR_(n),where n≥*** show that the local smooth solution to the heat flow of self-induced harmonic map will blow up at a finite time,provided that the initial map u0 is in a suitable nontrivial homotopy class with energy small enough.
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