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arXiv 2202.04868cs.LGcs.AIstat.ML
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理解深度协作多智能体强化学习中的值分解算法

Understanding Value Decomposition Algorithms in Deep Cooperative Multi-Agent Reinforcement Learning

Yale University(耶鲁大学);University of Oxford(牛津大学);Peking University(北京大学);BIGAI(北京通用人工智能研究院)

Zehao Dou, Jakub Grudzien Kuba, Yaodong Yang

摘要:

价值函数分解正在成为一种流行的经验法则,用于在合作游戏中扩展多智能体强化学习(MARL)。对于这样的分解规则,必须假设个体-全局最大值(IGM)原则;也就是说,每个代理的分解价值函数上的局部最大值必须等于联合价值函数上的全局最大值。然而,这一原则并不一定在一般情况下成立。因此,值分解算法的适用性被掩盖,其相应的收敛特性仍然未知。在本文中,我们首次尝试回答这些问题。具体来说,我们引入了一组合作博弈的价值分解方法找到他们的有效性,这是被称为可分解的游戏。在可分解博弈中,我们从理论上证明了应用多智能体拟合Q迭代算法(MA-FQI)将导致最优Q函数。在不可分解对策中,在Q函数每次迭代都需要投影到可分解函数空间的情况下,MA-FQI估计的Q函数仍能收敛到最优解。在这两种情况下,我们考虑实际深度神经网络的价值函数表示,并推导出相应的收敛速度。总之,我们的研究结果首次为MARL从业者提供了关于价值分解算法何时收敛以及为什么它们表现良好的理论见解。

英文摘要:

Value function decomposition is becoming a popular rule of thumb for scaling up multi-agent reinforcement learning (MARL) in cooperative games. For such a decomposition rule to hold, the assumption of the individual-global max (IGM) principle must be made; that is, the local maxima on the decomposed value function per every agent must amount to the global maximum on the joint value function. This principle, however, does not have to hold in general. As a result, the applicability of value decomposition algorithms is concealed and their corresponding convergence properties remain unknown. In this paper, we make the first effort to answer these questions. Specifically, we introduce the set of cooperative games in which the value decomposition methods find their validity, which is referred as decomposable games. In decomposable games, we theoretically prove that applying the multi-agent fitted Q-Iteration algorithm (MA-FQI) will lead to an optimal Q-function. In non-decomposable games, the estimated Q-function by MA-FQI can still converge to the optimum under the circumstance that the Q-function needs projecting into the decomposable function space at each iteration. In both settings, we consider value function representations by practical deep neural networks and derive their corresponding convergence rates. To summarize, our results, for the first time, offer theoretical insights for MARL practitioners in terms of when value decomposition algorithms converge and why they perform well.

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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