论文标题
带有原始二重动力学的随机编程：平均场游戏方法
Stochastic Programming with Primal-Dual Dynamics: A Mean-Field Game Approach
论文作者
论文摘要
这项研究介绍了针对能力网络设计的随机编程问题的原始二重动力学。事实证明，可以在代表网络容量的\ textit {此处和现在}变量上达成共识。主要的贡献是一种启发式方法，涉及将问题作为平均场地游戏的表述。平均场游戏中的每个代理都可以控制自己的原始偶二动态动态，并根据通信拓扑与邻近代理寻求共识。我们获得有关平均场平衡存在的理论结果。此外，我们证明了共识动态会融合，因此代理人同意其各自的微型网络的能力。最后，我们强调对控制和状态的惩罚如何影响平均场比赛中代理的动态。
This study addresses primal-dual dynamics for a stochastic programming problem for capacity network design. It is proven that consensus can be achieved on the \textit{here and now} variables which represent the capacity of the network. The main contribution is a heuristic approach which involves the formulation of the problem as a mean-field game. Every agent in the mean-field game has control over its own primal-dual dynamics and seeks consensus with neighboring agents according to a communication topology. We obtain theoretical results concerning the existence of a mean-field equilibrium. Moreover, we prove that the consensus dynamics converge such that the agents agree on the capacity of their respective micro-networks. Lastly, we emphasize how penalties on control and state influence the dynamics of agents in the mean-field game.
