Random Minimax Game Trees

Random Discrete Structures - The IMA Volumes in Mathematics and its Applications ◽

10.1007/978-1-4612-0719-1_5 ◽

1996 ◽

pp. 55-80 ◽

Cited By ~ 2

Author(s):

Luc Devroye ◽

Olivier Kamoun

Keyword(s):

Game Trees ◽

Minimax Game

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Searching minimax game trees under memory space constraint

Annals of Mathematics and Artificial Intelligence ◽

10.1007/bf01531075 ◽

1990 ◽

Vol 1 (1-4) ◽

pp. 141-153 ◽

Cited By ~ 3

Author(s):

Toshihide Ibaraki ◽

Yoshiroh Katoh

Keyword(s):

Space Constraint ◽

Memory Space ◽

Game Trees ◽

Minimax Game

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Structure theorems for game trees

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.082249599 ◽

2002 ◽

Vol 99 (13) ◽

pp. 9077-9080 ◽

Cited By ~ 13

Author(s):

S. Govindan ◽

R. Wilson

Keyword(s):

Game Trees ◽

Structure Theorems

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

Guidance, Navigation and Control ◽

10.1142/s2737480721500114 ◽

2021 ◽

pp. 2150011

Author(s):

Wei Dong ◽

Jianan Wang ◽

Chunyan Wang ◽

Zhenqiang Qi ◽

Zhengtao Ding

Keyword(s):

Reinforcement Learning ◽

Spanning Tree ◽

Learning Algorithm ◽

Control Policy ◽

Game Problem ◽

Algebraic Riccati Equation ◽

Multi Agent Systems ◽

Rank Condition ◽

Minimax Game ◽

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 reinforcement 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 effectiveness of the proposed method is demonstrated through a numerical simulation.

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