AI 中文总结
本文针对多集群聚合博弈的纳什均衡求解问题，提出带梯度外推的分布式镜像下降算法，在非欧几里得场景下实现$\tilde{O}(1/k)$收敛，经能源系统需求响应算例验证有效。
AI 中文摘要
本文研究一类兼具合作与竞争特性的多集群聚合博弈，其中每个智能体的代价函数依赖于自身策略及所有智能体策略的总和。针对此类博弈在非欧几里得场景下的纳什均衡求解问题，本文提出一种在时变集群内及集群间网络上运行的带梯度外推的分布式镜像下降算法。镜像下降框架采用通用的Bregman散度作为距离度量，相比基于欧几里得的方法具备更强灵活性；梯度外推则利用历史梯度信息提升收敛性能。在由Bregman散度刻画的限制强单调性条件下，本文证明了所提算法的收敛性，且在步长及参数选取合适时，算法达到$\tilde{O}(1/k)$的收敛速率。最后，通过能源系统需求响应的算例验证了所提算法的有效性。
英文摘要
This paper studies a class of multi-cluster aggregative games characterized by the coexistence of cooperation and competition, where each agent's cost function depends on its own strategy and the aggregate of all agents' strategies. To address the Nash equilibrium seeking problem for such games in the non-Euclidean setting, a distributed mirror descent algorithm with gradient extrapolation is proposed over time-varying intra-cluster and inter-cluster networks. The mirror descent framework employs a general Bregman divergence as the distance measure, providing greater flexibility than Euclidean-based methods, while gradient extrapolation exploits historical gradient information to improve convergence performance. Under the restricted strong monotonicity characterized by the Bregman divergence, the convergence of the proposed algorithm is established, and it achieves the $\mathcal{O}(1/k)$ convergence rate with the appropriately selected step-size and parameters. Finally, the effectiveness of the proposed algorithm is verified by an example on the demand response of energy systems.
