论文标题
在线分布式算法，用于在动态环境中寻求广义的NASH平衡
Online distributed algorithms for seeking generalized Nash equilibria in dynamic environments
论文作者
论文摘要
在本文中，我们研究了在动态环境中分布的广义NASH均衡寻求非合作游戏的问题。游戏中的每个玩家都旨在最大程度地减少其时间变化的成本功能，但要遵守本地动作集。所有玩家的动作集都通过共享的凸不平等约束结合在一起。每个玩家只能访问其自身的成本函数，其自身设置的约束和不平等约束的本地块，并且只能通过连接的图形与邻居进行通信。此外，玩家对未来成本功能没有事先了解。为了解决这个问题，根据共识算法和原始偶尔策略提出了在线分布式算法。算法的性能是通过使用动态后悔来衡量的。在对图和成本函数的轻度假设下，我们证明，如果变异性纳什均衡序列的偏差在一定速度内增加，那么遗憾以及违反不平等约束的行为会增长。提出了模拟以证明我们理论结果的有效性。
In this paper, we study the distributed generalized Nash equilibrium seeking problem of non-cooperative games in dynamic environments. Each player in the game aims to minimize its own time-varying cost function subject to a local action set. The action sets of all players are coupled through a shared convex inequality constraint. Each player can only have access to its own cost function, its own set constraint and a local block of the inequality constraint, and can only communicate with its neighbours via a connected graph. Moreover, players do not have prior knowledge of their future cost functions. To address this problem, an online distributed algorithm is proposed based on consensus algorithms and a primal-dual strategy. Performance of the algorithm is measured by using dynamic regrets. Under mild assumptions on graphs and cost functions, we prove that if the deviation of variational generalized Nash equilibrium sequence increases within a certain rate, then the regrets, as well as the violation of inequality constraint, grow sublinearly. A simulation is presented to demonstrate the effectiveness of our theoretical results.
