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arXiv 2202.04129cs.LGcs.GTcs.MAmath.OC
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大规模马尔可夫势博弈的独立策略梯度:更快的速率、函数逼近和博弈无关收敛

Independent Policy Gradient for Large-Scale Markov Potential Games: Sharper Rates, Function Approximation, and Game-Agnostic Convergence

University of Southern California(南加州大学);Massachusetts Institute of Technology(麻省理工学院)

Dongsheng Ding, Chen-Yu Wei, Kaiqing Zhang, Mihailo R. Jovanović

摘要:

研究了马尔可夫势博弈中多智能体强化学习(RL)问题的策略梯度方法的全局非渐近收敛性.为了学习纳什均衡的MPG中的状态空间的大小和/或玩家的数量可以是非常大的,我们提出了新的独立的策略梯度算法,是由所有玩家串联运行。当梯度评估中没有不确定性时,我们证明了我们的算法找到了具有$O(1/ε^2)$迭代复杂度的$ε$ -纳什均衡,该迭代复杂度不显式地依赖于状态空间大小。当精确的梯度是不可用的,我们建立$O(1/ε^5)$样本复杂性界在一个潜在的无限大的状态空间的基于样本的算法,利用函数逼近。此外,我们确定了一类独立的策略梯度算法,享有收敛的零和马尔可夫游戏和马尔可夫合作游戏的球员,是不知道正在玩的游戏类型。最后,我们提供了计算实验来证实我们的理论发展的优点和有效性。

英文摘要:

We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPG). To learn a Nash equilibrium of an MPG in which the size of state space and/or the number of players can be very large, we propose new independent policy gradient algorithms that are run by all players in tandem. When there is no uncertainty in the gradient evaluation, we show that our algorithm finds an $ε$-Nash equilibrium with $O(1/ε^2)$ iteration complexity which does not explicitly depend on the state space size. When the exact gradient is not available, we establish $O(1/ε^5)$ sample complexity bound in a potentially infinitely large state space for a sample-based algorithm that utilizes function approximation. Moreover, we identify a class of independent policy gradient algorithms that enjoys convergence for both zero-sum Markov games and Markov cooperative games with the players that are oblivious to the types of games being played. Finally, we provide computational experiments to corroborate the merits and the effectiveness of our theoretical developments.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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