Grap hical Minimax Game and Off-Policy Reinforcement Learning for Heterogeneous MASs with Spanning Tree Condition

In this paper,the optimal consensus control problem is investigated for heterogeneous linear multi-agent systems(MASs)with spanning tree condition based on game theory and rein-forcement learning.First,the graphical minimax game algebraic Riccati equation(ARE)is derived by converting the consensus problem into a zero-sum game problem between each agent and its neighbors.The asymptotic stability and minimax validation of the closed-loop systems are proved theoretically.Then,a data-driven off-policy reinforcement learning algorithm is proposed to online learn the optimal control policy without the information of the system dynamics.A certain rank condition is established to guarantee the convergence of the proposed algorithm to the unique solution of the ARE.Finally,the e®ectiveness of the proposed method is demonstrated through a numerical simulation.

Research on Different Heuristics for Minimax Algorithm Insight from Connect-4 Game

Minimax algorithm and machine learning technologies have been studied for decades to reach an ideal optimization in game areas such as chess and backgammon. In these fields, several generations try to optimize the code for pruning and effectiveness of evaluation function. Thus, there are well-armed algorithms to deal with various sophisticated situations in gaming occasion. However, as a traditional zero-sum game, Connect-4 receives less attention compared with the other members of its zero-sum family using traditional minimax algorithm. In recent years, new generation of heuristics is created to address this problem based on research conclusions, expertise and gaming experiences. However, this paper mainly introduced a self-developed heuristics supported by well-demonstrated result from researches and our own experiences which fighting against the available version of Connect-4 system online. While most previous works focused on winning algorithms and knowledge based approaches, we complement these works with analysis of heuristics. We have conducted three experiments on the relationship among functionality, depth of searching and number of features and doing contrastive test with sample online. Different from the sample based on summarized experience and generalized features, our heuristics have a basic concentration on detailed connection between pieces on board. By analysing the winning percentages when our version fights against the online sample with different searching depths, we find that our heuristics with minimax algorithm is perfect on the early stages of the zero-sum game playing. Because some nodes in the game tree have no influence on the final decision of minimax algorithm, we use alpha-beta pruning to decrease the number of meaningless node which greatly increases the minimax efficiency. During the contrastive experiment with the online sample, this paper also verifies basic characters of the minimax algorithm including depths and quantity of features. According to the experiment, these two characters can both effect the decision for each step and none of them can be absolutely in charge. Besides, we also explore some potential future issues in Connect-4 game optimization such as precise adjustment on heuristic values and inefficiency pruning on the search tree.

Statistical Learning in Game Theory

In economics, buyers and sellers are usually the main sides in a market. Game theory can perfectly model decisions behind each “player” and calculate an outcome that benefits both sides. However, the use of game theory is not lim-ited to economics. In this paper, I will introduce the mathematical model of general sum game, solutions and theorems surrounding game theory, and its real life applications in many different scenarios.

不可达系统的鲁棒贝叶斯估计方法

本文针对模型扰动下的不可达系统,提出了一种新的针对退化分布下的极大极小博弈问题的求解和证明方法.首先,文章将有相对熵约束的极大极小博弈问题转换成了一个无约束的拉格朗日函数,并找到其在均值和奇异的方差矩阵方向上都为严格凹函数的条件;其次,本文通过求解其均值和方差的极大值,得到所对应的鲁棒贝叶斯估计器和奇异的扰动状态误差协方差矩阵;最后,文章证明存在一个唯一的拉格朗日乘子满足其约束条件.微机电系统加速度计漂移估计仿真结果表明对所提算法的有效性.

一个关于流动能量耗散率的minimax变分原理

流动耗散率是湍流理论的核心概念之一.Doering-Constantin变分原理刻画了流动耗散率的上确界(最大值).在该文的研究中,首先基于优化理论的视角,Doering-Constantin的变分原理被改写为一个不可压缩剪切流耗散率的minimax型的变分原理.其次,博弈论中的Kakutanim inimax定理给出该变分原理中minimizing和maximizing计算过程可交换的一个充分条件.这个结果不仅从一个新的角度揭示了谱约束的内涵,也为Doering-Constantin变分原理和Howard-Busse统计理论的等价性从博弈论的角度提供了理论基础.

周期时变不确定性线性系统的MINIMAX控制方法

应用约束最优化方法和微分对策理论 ,讨论周期时变不确定性线性系统在范数有界外部干扰情况下的 MINIMAX控制和参数摄动情况下的 MINIMAX控制 .问题可解的充分条件是一类 Riccati微分方程具有稳定化解 ,且关于最坏扰动的某个附加条件满足相应的 MINI-MAX控制恰为一个线性状态反馈 .此外 。

一个新的拓扑Minimax定理

本文证明了一个新的拓扑Minimax定理,它不要求Y是强连通的,程曹宗与林有浩的结果是我们定理的推论。

Minimax principle on energy dissipation of incompressible shear flow

The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin＇s variational principle characterizes the upper bounds （maxi- mum） of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin＇s formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin＇s variational principle and Howard- Busse＇s statistical turbulence theory.

Minimax State Estimator for Uncertain Systems with L_2 Bounded Constraint

Minimax state estimation is discussed for uncerttain systems with L2 bounded constraint. A dtaity relation-equality is introduced to estimate terminal state variabes x(T) by measurable outputs . hawing a game theory, opti-mal estimation leads to a simple solution. LQL control scheme, is further discussed to make it rational in the actual application.

Generative Adversarial Networks for Secure Data Transmission in Wireless Network

In this paper,a communication model in cognitive radios is developed and uses machine learning to learn the dynamics of jamming attacks in cognitive radios.It is designed further to make their transmission decision that automati-cally adapts to the transmission dynamics to mitigate the launched jamming attacks.The generative adversarial learning neural network(GALNN)or genera-tive dynamic neural network(GDNN)automatically learns with the synthesized training data(training)with a generator and discriminator type neural networks that encompass minimax game theory.The elimination of the jamming attack is carried out with the assistance of the defense strategies and with an increased detection rate in the generative adversarial network(GAN).The GDNN with game theory is designed to validate the channel condition with the cross entropy loss function and back-propagation algorithm,which improves the communica-tion reliability in the network.The simulation is conducted in NS2.34 tool against several performance metrics to reduce the misdetection rate and false alarm rates.The results show that the GDNN obtains an increased rate of successful transmis-sion by taking optimal actions to act as a defense mechanism to mislead the jam-mer,where the jammer makes high misclassification errors on transmission dynamics.

Science Letters:A minimax optimal control strategy for uncertain quasi-Hamiltonian systems

A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct the system energy control,the partially averaged It stochastic differential equations for the energy processes are first derived by using the stochastic averaging method for quasi-Hamiltonian systems. Combining the above equations with an appropriate performance index,the proposed strategy is searching for an optimal worst-case controller by solving a stochastic differential game problem. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs(HJI) equation. Numerical results for a controlled and stochastically excited Duffing oscillator with uncertain disturbances exhibit the efficacy of the proposed control strategy.

基于极小极大博弈的水军识别算法研究

随着互联网的发展,用户越来越多地在线上完成购物、订餐,并倾向于先参考线上评论。评论对用户决策的重要导向作用催生了网络水军。网络水军会为了自身利益或其他不良动机,发布与实际体验不相符的评价,且会随时调整自己的策略来逃避平台的识别。现提出一个基于行为特征的水军识别算法(FBS),并将FBS加入到极小极大博弈,在这个博弈中,水军与识别器相互竞争,将博弈转换为两个相互依赖的马尔可夫决策过程,不断优化各自的策略,最终得到一个当前场景下最优的识别器。与当前先进的水军识别算法对比,性能有了明显提升,在公开数据集YelpChi上实际效应可以达到3.69。

合作竞争博弈模型及其应用

合作竞争已成为当今经济发展战略的大趋势 ,本文通过合作博弈与竞争博弈的优劣对比 ,提出合作竞争博弈模型 ,并用一类 Minimax定理求解合作竞争博弈均衡 .同时以非对称双寡头合作竞争产量博弈为例 。

对称成本企业合作竞争博弈分析

企业间的合作竞争已成为当今世界经济发展战略的大趋势,本文采用Minimax定理来进行合作竞争的战略决策,该决策战略能确保均衡点处达到较高满意度的企业数量较多。将Minimax定理用于线性逆需求对称成本企业合作竞争的产量战略博弈,并与完全竞争市场中的NASH博弈均衡和完全合作均衡进行了对比,最后提出了对付非合作行为的战略。

极小极大值理论的历史发展

就博弈论早期史这一问题,采用考证原著的方法,针对极小极大值理论早期发展的历史进行了研究。认为:历史上第一个极小极大值解是法国数学家瓦德哥锐于1713年得到的,但在此后的两个世纪中,这一结果一直没有引起人们的注意。直到20世纪20年代,波莱尔在研究二人零和博弈时才重新得出了极小极大值解的概念,而极小极大值定理的正式提出和证明则是由冯·诺伊曼于1928年完成的。此后,这一定理的证明又进一步得到了简化和完善。

突发事件下供应链企业间援助行为分析

通过对比分析,证明了援助策略能够提高供应链的绩效,并运用极小极大后悔方法求出了只知道突发事件造成损失的范围情况下零售商的最优援助资金额,最后运用动机公平博弈理论分析了供应商"投桃报李"特征对援助效果的影响。

考虑不确定性和多主体博弈的增量配电网源网荷协同规划方法

在对增量配电网进行规划时,如何根据不同利益主体的市场行为获取最优的决策方案是目前亟需解决的重要问题。针对该问题,该文通过引入虚拟博弈者"大自然",实现了博弈理论和鲁棒优化的深度融合,提出一种考虑不确定性和多主体博弈的增量配电网源网荷协同规划方法。首先,分别构建DG投资运营商、配电网投资运营商和电力用户不同利益主体的规划决策模型;然后根据三者的传递关系分析分布式电源(distributed generation,DG)投资运营商和配电网投资运营商之间的静态博弈行为;同时采用鲁棒优化处理DG出力的不确定性,并引入虚拟博弈者"大自然",研究其与配电网投资运营商之间的动态博弈行为;在此基础上提出动–静态联合博弈规划模型,最后结合迭代搜索算法和极大极小值法对上述模型进行求解。仿真结果验证了文中方法的正确性和有效性。

博弈树搜索算法设计和分析

本文提出了博弈树搜索SSS~*算法的两种改进算法BS~*和DS~*算法,给出了BS~*和DS~*搜索博弈树端结点的充分必要条件,并由此证明了,如果能估计一个合适的上界,则BS~*算法优于SSS~*算法,同时还证明了DS~*算法优于α-β算法,论述了DS~*算法搜索深度为奇数的博弈树时,在一般情况下也优于SSS~*算法,且这两种算法都降低了存储开销。

一般化两人零和模糊对策

定义一般化两人零和模糊对策,分别对具有纯策略和混合策略的一般化两人零和模糊对策进行研究,得到相应的最小最大值定理,以及一些与经典矩阵对策相类似的结果。

FC-空间的一个极大极小不等式及应用

运用FC-空间中的一个极大极小不等式,对FC-空间中的抽象变分不等式和似变分不等式解的存在性,Ky Fan型截口定理,以及具有扰动的二人零和博弈存在性进行研究,从而得到没有线性结构的FC-空间中一些新的抽象变分不等式和似变分不等式解的存在性结果和一Ky Fan型截口定理.最后得到了一个具有扰动的二人零和博弈的存在性结果.