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Multi-agent graphical games with input constraints: an online learning solution
TianxiangWANG,BingchangWANG,YongLIANG
0
(School of Control Science and Engineering, Shandong University, Jinan Shandong 250061, China)
摘要:
This paper studies an online iterative algorithm for solving discrete-time multi-agent dynamic graphical games with input constraints. In order to obtain the optimal strategy of each agent, it is necessary to solve a set of coupled Hamilton-Jacobi-Bellman (HJB) equations. It is very difficult to solve HJB equations by the traditional method. The relevant game problem will become more complex if the control input of each agent in the dynamic graphical game is constrained. In this paper, an online iterative algorithm is proposed to find the online solution to dynamic graphical game without the need for drift dynamics of agents. Actually, this algorithm is to find the optimal solution of Bellman equations online. This solution employs a distributed policy iteration process, using only the local information available to each agent. It can be proved that under certain conditions, when each agent updates its own strategy simultaneously, the whole multi-agent system will reach Nash equilibrium. In the process of algorithm implementation, for each agent, two layers of neural networks are used to fit the value function and control strategy, respectively. Finally, a simulation example is given to show the effectiveness of our method.
关键词:  Actor-critic algorithm, differential games, input constraints, neural network (NN), reinforcement learning (RL)
DOI:https://doi.org/10.1007/s11768-020-0013-6
基金项目:This work was supported by the National Natural Science Foundation of China (Nos. 61773241, 61973183) and the Shandong Provincial Natural Science Foundation (No. ZR2019MF041).
Multi-agent graphical games with input constraints: an online learning solution
Tianxiang WANG,Bingchang WANG,Yong LIANG
(School of Control Science and Engineering, Shandong University, Jinan Shandong 250061, China)
Abstract:
This paper studies an online iterative algorithm for solving discrete-time multi-agent dynamic graphical games with input constraints. In order to obtain the optimal strategy of each agent, it is necessary to solve a set of coupled Hamilton-Jacobi-Bellman (HJB) equations. It is very difficult to solve HJB equations by the traditional method. The relevant game problem will become more complex if the control input of each agent in the dynamic graphical game is constrained. In this paper, an online iterative algorithm is proposed to find the online solution to dynamic graphical game without the need for drift dynamics of agents. Actually, this algorithm is to find the optimal solution of Bellman equations online. This solution employs a distributed policy iteration process, using only the local information available to each agent. It can be proved that under certain conditions, when each agent updates its own strategy simultaneously, the whole multi-agent system will reach Nash equilibrium. In the process of algorithm implementation, for each agent, two layers of neural networks are used to fit the value function and control strategy, respectively. Finally, a simulation example is given to show the effectiveness of our method.
Key words:  Actor-critic algorithm, differential games, input constraints, neural network (NN), reinforcement learning (RL)