Learning in Two-Player Matrix Games by Policy Gradient Lagging Anchor

Shiyao DING  Toshimitsu USHIO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.4   pp.708-711
Publication Date: 2019/04/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.708
Type of Manuscript: LETTER
Category: Mathematical Systems Science
reinforcement learning,  policy gradient,  multi-agent systems,  matrix game,  

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It is known that policy gradient algorithm can not guarantee the convergence to a Nash equilibrium in mixed policies when it is applied in matrix games. To overcome this problem, we propose a novel multi-agent reinforcement learning (MARL) algorithm called a policy gradient lagging anchor (PGLA) algorithm. And we prove that the agents' policies can converge to a Nash equilibrium in mixed policies by using the PGLA algorithm in two-player two-action matrix games. By simulation, we confirm the convergence and also show that the PGLA algorithm has a better convergence than the LR-I lagging anchor algorithm.