针对大规模动态博弈,提出高效连续时间策略优化方法。
Policy Optimization for Continuous-time Linear-Quadratic Graphon Mean Field Games
- 用共享斜率+个体截距的线性策略参数化,提升可扩展性。
- 算法线性收敛至纳什均衡,理论证明全局最优性。
- 适合研究大规模异质玩家博弈,尤其适用于复杂网络结构。
多智能体强化学习在大规模动态博弈中面临显著可扩展性挑战。图函数平均场博弈(GMFGs)提供了一个合理的近似框架,能够捕捉玩家间的异质性。本文提出并分析了针对连续时间、有限时域线性二次型GMFGs的策略优化框架。利用GMFGs的结构性质,设计了一种高效的策略参数化方法:每个玩家的策略表示为私有状态的仿射函数,共享斜率函数,具有玩家特异的截距。我们开发了一种双层优化算法,交替进行固定群体分布下的策略梯度更新以计算最佳响应,以及基于所得策略的分布更新。我们证明了策略梯度步骤在线性收敛到最佳响应策略,并建立了整体算法全局收敛至纳什均衡。分析依赖于对无限维策略空间的新颖景观表征。数值实验表明,该算法在不同图函数结构、噪声水平和动作频率下均表现出良好的收敛性和鲁棒性。
原文摘要 · Abstract (English)
Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating such games while capturing heterogeneity among players. In this paper, we propose and analyze a policy optimization framework for continuous-time, finite-horizon linear-quadratic GMFGs. Exploiting the structural properties of GMFGs, we design an efficient policy parameterization in which each player's policy is represented as an affine function of their private state, with a shared slope function and player-specific intercepts. We develop a bilevel optimization algorithm that alternates between policy gradient updates for best-response computation under a fixed population distribution, and distribution updates using the resulting policies. We prove linear convergence of the policy gradient steps to best-response policies and establish global convergence of the overall algorithm to the Nash equilibrium. The analysis relies on novel landscape characterizations over infinite-dimensional policy spaces. Numerical experiments demonstrate the convergence and robustness of the proposed algorithm under varying graphon structures, noise levels, and action frequencies.
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