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Accelerated Value Iteration for Nonlinear zero-sum games with Convergence Guarantee

Guidance, Navigation and Control 2024年第1期4卷 121-148页

作者： Yuan Wang Mingming Zhao Nan Liu Ding Wang Faculty of Information Technology Beijing University of Technology Beijing 100124P.R.China Beijing Key Laboratory of Computational Intelligence and Intelligent System Beijing University of Technology Beijing 100124P.R.China Beijing Institute of Artificial Intelligence Beijing University of Technology Beijing 100124P.R.China Beijing Laboratory of Smart Environmental Protection Beijing University of Technology Beijing 100124P.R.China

In this paper,an accelerated value iteration(VI)algorithm is established to solve the zero-sum game problem with convergence ***,inspired by the successive over relaxation theory,the convergence rate of the iterative value function sequence is accelerated significantly with the relaxation ***,the convergence and monotonicity of the value function sequence are analyzed under different ranges of the relaxation ***,two practical approaches,namely the integrated scheme and the relaxation function,are introduced into the accelerated VI algorithm to guarantee the convergence of the iterative value function sequence for zero-sum *** integrated scheme consists of the accelerated stage and the convergence stage,and the relaxation function can adjust the value of the relaxation ***,including the autopilot controller,the fantastic performance of the accelerated VI algorithm is verified through two examples with practical physical backgrounds.

关键词： Adaptive dynamic programming convergence rate value iteration zero-sum games

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Polynomial Time Method for Solving Nash Equilibria of zero-sum games

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American Journal of Computational Mathematics 2021年第1期11卷 23-30页

作者： Yoshihiro Tanaka Mitsuru Togashi Faculty of Economics and Business Hokkaido University Sapporo Japan Graduate School of Accountancy Waseda University Tokyo Japan

There are a few studies that focus on solution methods for finding a Nash equilibrium of zero-sum games. We discuss the use of Karmarkar’s interior point method to solve the Nash equilibrium problems of a zero-sum game, and prove that it is theoretically a polynomial time algorithm. We implement the Karmarkar method, and a preliminary computational result shows that it performs well for zero-sum games. We also mention an affine scaling method that would help us compute Nash equilibria of general zero-sum games effectively.

关键词： zero-sum games Nash Equilibria Karmarkar’s Method Polynomial Time

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A survey of decision making in adversarial games

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Science China(Information Sciences) 2024年第4期67卷 85-112页

作者： Xiuxian LI Min MENG Yiguang HONG Jie CHEN College of Electronics and Information Engineering Tongji University Shanghai Research Institute for Intelligent Autonomous Systems

In many practical applications, such as poker, chess, drug interdiction, cybersecurity, and national defense, players often have adversarial stances, i.e., the selfish actions of each player inevitably or intentionally inflict loss or wreak havoc on other players. Therefore, adversarial games are important in realworld applications. However, only special adversarial games, such as Bayesian games, are reviewed in the literature. In this respect, this study aims to provide a systematic survey of three main game models widely employed in adversarial games, i.e., zero-sum normal-form and extensive-form games, Stackelberg(security) games, and zero-sum differential games, from an array of perspectives, including basic knowledge of game models,(approximate) equilibrium concepts, problem classifications, research frontiers,(approximate) optimal strategy-seeking techniques, prevailing algorithms, and practical applications. Finally, promising future research directions are also discussed for relevant adversarial games.

关键词： adversarial games zero-sum games Stackelberg games differential games Nash equilibrium correlated equilibrium regret

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Sensing,Coordination and Control in Adversarial Environments with Limited Actions

Sensing,Coordination and Control in Adversarial Environments...

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第三十届中国控制会议

作者： BASAR Tamer Coordinated Science Laboratory University of Illinois1308 West MainUrbanaIL 61801U.S.A.

ISBN: (纸本)9789881725592

＜正＞This Plenary Talk will introduce a paradigm for networked control systems operating in an uncertain environment, where the number of instants when a controller communicates with the plant（for example sends control signals to the plant） and the number of instants sensors communicate plant information to the controller are severely restricted,and both the sensors and the controllers have to make most of the few opportunities they *** of both optimal controller and optimal sensor policies under such nontraditional restrictions will be discussed,and the framework will be extended to scenarios where the communication at both links could be disrupted by an adversary,which also acts *** this latter case,what is sought for is not an optimal solution,but rather a saddle-point solution between two opposing *** both cases,the optimal or saddle-point policies are of the threshold type.

关键词： Networked systems and control adversarial action threshold-type policies zero-sum games saddle-point policies

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对弈必胜策略的符号化模型检测

对弈必胜策略的符号化模型检测

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2006年全国理论计算机科学学术年会

作者：何青骆翔宇苏开乐中山大学计算机科学系中山大学计算机科学系中山大学计算机科学系

＜正＞1 引言在对弈问题的研究中,人们一直都在探询这样的问题:对弈中的某一方是否存在必胜策略,也就是说无论对手如何行棋,该方是否总是能够战胜对手。从搜索技术的角度来看,这将需要对棋局的状态空间进行穷举搜索,因此启发式搜索技术... 详细信息

＜正＞1 引言在对弈问题的研究中,人们一直都在探询这样的问题:对弈中的某一方是否存在必胜策略,也就是说无论对手如何行棋,该方是否总是能够战胜对手。从搜索技术的角度来看,这将需要对棋局的状态空间进行穷举搜索,因此启发式搜索技术无法很好地解决这个问题。然而从形式化方法的角度来看,这个问题可归结为棋局模型中的形式化验证问题,即

关键词： Symbolic model checking BDDs zero-sum games Winning strategy

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