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arXiv 2202.04868cs.LGcs.AIstat.ML
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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

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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