通过双重增广算子分裂方法实现网络中部分决策信息下的分布式 GNE 求解
Distributed GNE seeking under partial-decision information over networks via a doubly-augmented operator splitting approach
AI总结：
针对部分决策信息下的共享耦合约束博弈，提出基于双重增广变量与单调算子分裂的单层分布式算法，实现原对偶完全分布式并以固定步长收敛至变分 GNE。
摘要：
我们考虑在具有共享耦合约束的博弈中，通过网络分布式计算广义纳什均衡（GNE）。现有方法要求每个参与者都能完全获取对手的决策。本文假设参与者仅拥有部分决策信息，并能够通过任意无向图与其邻居通信。通过原对偶分析，我们将该问题重构为寻找单调算子之和的零点。为分布式化该问题，我们对变量进行双重增广，使每个参与者都拥有局部决策估计以及 Lagrange 乘子的局部副本。我们提出一种单层算法，该算法在原变量和对偶变量方面均完全分布式。通过将其重构为针对一对双重增广单调算子的前向-后向迭代，我们证明了该算法在固定步长下收敛到变分 GNE。
英文摘要：
We consider distributed computation of generalized Nash equilibrium (GNE) over networks, in games with shared coupling constraints. Existing methods require that each player has full access to opponents' decisions. In this paper, we assume that players have only partial-decision information, and can communicate with their neighbours over an arbitrary undirected graph. We recast the problem as that of finding a zero of a sum of monotone operators through primal-dual analysis. To distribute the problem, we doubly augment variables, so that each player has local decision estimates and local copies of Lagrangian multipliers. We introduce a single-layer algorithm, fully distributed with respect to both primal and dual variables. We show its convergence to a variational GNE with fixed step-sizes, by reformulating it as a forward-backward iteration for a pair of doubly-augmented monotone operators.
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