Individual Q-learning in normal form games

Leslie, David S. and Collins, E. J. (2005) Individual Q-learning in normal form games. SIAM Journal on Control and Optimization, 44 (2). pp. 495-514. ISSN 0363-0129

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The single-agent multi-armed bandit problem can be solved by an agent that learns the values of each action using reinforcement learning. However, the multi-agent version of the problem, the iterated normal form game, presents a more complex challenge, since the rewards available to each agent depend on the strategies of the others. We consider the behavior of value-based learning agents in this situation, and show that such agents cannot generally play at a Nash equilibrium, although if smooth best responses are used, a Nash distribution can be reached. We introduce a particular value-based learning algorithm, which we call individual Q-learning, and use stochastic approximation to study the asymptotic behavior, showing that strategies will converge to Nash distribution almost surely in 2-player zero-sum games and 2-player partnership games. Player-dependent learning rates are then considered, and it is shown that this extension converges in some games for which many algorithms, including the basic algorithm initially considered, fail to converge.

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Journal Article
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SIAM Journal on Control and Optimization
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12 Sep 2014 11:28
Last Modified:
21 Sep 2023 01:45