This paper is concerned with the distributed generalized Nash equilibrium (GNE) tracking problem of noncooperative games in dynamic environments, where the cost function and/or the coupled constraint function are time-varying and revealed to each agent after it makes a decision. We first consider the case without coupled constraints and propose a distributed inertial online game (D-IOG) algorithm based on the mirror descent method. The proposed algorithm is capable of tracking Nash equilibrium (NE) through a time-varying communication graph and has the potential of achieving a low average regret. With an appropriate non-increasing stepsize sequence and an inertial parameter, the regrets can grow sublinearly if the deviation of the NE sequence grows sublinearly. Second, the time-varying coupled constraints are further investigated, and a modified D-IOG algorithm for tracking GNE is proposed based on the primal-dual and mirror descent methods. Then, the upper bounds of regrets and constraint violation are derived. Moreover, inertia and two information transmission modes are discussed. Finally, two simulation examples are provided to illustrate the effectiveness of the D-IOG algorithms.

中文翻译：

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跟踪广义纳什均衡的分布式惯性在线博弈算法

本文关注动态环境中非合作博弈的分布式广义纳什均衡（GNE）跟踪问题，其中成本函数和/或耦合约束函数是时变的，并在每个智能体做出决策后向其揭示。我们首先考虑没有耦合约束的情况，并提出一种基于镜像下降法的分布式惯性在线游戏（D-IOG）算法。所提出的算法能够通过时变通信图跟踪纳什均衡（NE），并且有可能实现低平均后悔。使用适当的非递增步长序列和惯性参数，如果 NE 序列的偏差呈次线性增长，则遗憾会呈次线性增长。其次，进一步研究了时变耦合约束，并基于原对偶法和镜像下降法提出了一种改进的D-IOG跟踪GNE算法。然后，导出遗憾和违反约束的上限。此外，还讨论了惯性和两种信息传输模式。最后，提供两个仿真例子来说明D-IOG算法的有效性。