arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2409.18152cs.GTcs.LGmath.OC
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有限空间平均场类型博弈的强化学习

Reinforcement Learning for Finite Space Mean-Field Type Games

Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning(上海前沿科学中心人工智能与深度学习中心);NYU Shanghai(纽约大学上海校区);NYU Center for Data Science(纽约大学数据科学中心);NYU-ECNU Institute of Mathematical Sciences(纽约大学-东华大学数学科学研究所)

Kai Shao, Jiacheng Shen, Mathieu Laurière

AI总结:

针对有限空间平均场类型博弈缺乏可扩展计算方法的问题,提出基于量化与Nash Q-learning及深度强化学习的算法,并证明近似均衡与实验有效性。

摘要:

平均场类型博弈(MFTG)描述大型联盟之间的 Nash 均衡:每个联盟由连续统的合作智能体组成,这些智能体在与有限数量的其他联盟进行非合作交互的同时,最大化其所在联盟的平均奖励。尽管相关理论已得到广泛发展,但我们仍缺乏高效且可扩展的计算方法。本文在具有一般动态和奖励函数的有限空间设定下,为此类博弈开发强化学习方法。我们首先证明 MFTG 解可在有限规模联盟博弈中产生近似 Nash 均衡。随后提出两种算法:第一种基于平均场空间的量化和 Nash Q-learning,并给出收敛性与稳定性分析;之后提出一种深度强化学习算法,可扩展至更大的空间。在4个环境、平均场分布维度最高达200的数值实验中,所提方法展现出可扩展性和效率。

英文摘要:

Mean field type games (MFTGs) describe Nash equilibria between large coalitions: each coalition consists of a continuum of cooperative agents who maximize the average reward of their coalition while interacting non-cooperatively with a finite number of other coalitions. Although the theory has been extensively developed, we are still lacking efficient and scalable computational methods. Here, we develop reinforcement learning methods for such games in a finite space setting with general dynamics and reward functions. We start by proving that the MFTG solution yields approximate Nash equilibria in finite-size coalition games. We then propose two algorithms. The first is based on the quantization of mean-field spaces and Nash Q-learning. We provide convergence and stability analysis. We then propose a deep reinforcement learning algorithm, which can scale to larger spaces. Numerical experiments in 4 environments with mean-field distributions of dimension up to $200$ show the scalability and efficiency of the proposed method.

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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