无界随机博弈中基于高斯过程的均衡学习算法
Equilibrium Learning in Unbounded Stochastic Games with Gaussian Transitions
arXiv 上这篇论文讲怎么在状态无界的多人随机博弈里学 Nash 均衡，用单条轨迹加 GP 建模，理论证明和数值实验都有，做博弈论强化学习的可以看看。
论文研究折扣一般和随机博弈，动作集紧致但状态空间无界，系统漂移项未知且受高斯转移噪声影响。方法用单条连续轨迹更新漂移的 Gaussian-process 模型，并迭代求解逐步细化的有限博弈。理论证明均衡选择的稳定性加上转移模型的一致 KL 精度，足以保证原始博弈中价值的区域一致收敛和近似 Nash 行为。GP 估计的收敛速率由后验不确定性、核信息增益和联合状态维度共同控制，数值实验验证了核选择与维度对收敛的影响。
Equilibrium Learning in Unbounded Stochastic Games with Gaussian Transitions
Learning equilibria from data is difficult when several decision makers interact indefinitely and the system state has no prescribed bounds. We examine discounted general-sum stochastic games with compact action sets and an unknown nonlinear drift observed through Gaussian transition noise. The proposed procedure uses a single uninterrupted trajectory to update Gaussian-process models of the drift and to solve successively refined finite games. We prove a perturbation result showing that stability of equilibrium selection, together with uniform KL accuracy of Gaussian transition models, is sufficient for regional uniform convergence of the induced values and approximate Nash behavior in the original game. The region specifies where the guarantees are evaluated; strategies and dynamics continue to act on the entire Euclidean state space. For GP estimators, simultaneous confidence bounds yield a rate controlled by posterior uncertainty, kernel information gain, and joint-state dimension. Numerical studies illustrate how kernel choice and dimension appear in the predicted convergence behavior.