We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange information with some neighbors, although its cost function possibly depends on the strategies of all agents. The few existing methods build on projected pseudo-gradient dynamics, and require either double-layer iterations or conservative conditions on the step sizes. To overcome both these flaws and improve efficiency, we design the first fully-distributed single-layer algorithms based on proximal best-response. Our schemes are fixed-step and allow for inexact updates, which is crucial for reducing the computational complexity. Under standard assumptions on the game primitives, we establish convergence to a variational equilibrium (with linear rate for games without coupling constraints) by recasting our algorithms as proximal-point methods, opportunely preconditioned to distribute the computation among the agents. Since our analysis hinges on a restricted monotonicity property, we also provide new general results that significantly extend the domain of applicability of proximal-point methods. Besides, the operator-theoretic approach favors the implementation of provably correct acceleration schemes that can further improve the convergence speed. Finally, the potential of our algorithms is demonstrated numerically, revealing much faster convergence with respect to projected pseudo-gradient methods and validating our theoretical findings.
翻译:我们处理在局部决定信息情景中寻求问题的普世纳什均衡问题,即每个代理商只能与某些邻居交流信息,尽管其成本功能可能取决于所有代理商的战略。少数现有方法以预测的假梯度动态为基础,要求使用双层迭代或阶梯尺寸的保守条件。为了克服这些缺陷并提高效率,我们设计了第一个完全分布的单层算法,其依据是准最佳反应。我们的计划是固定的,允许不精确的更新,这对降低计算复杂性至关重要。在游戏原始人的标准假设下,我们通过将我们的算法重新表述为准点方法,或者需要双层迭代,或者需要双层迭代,或者需要一步尺寸的保守条件。为了克服这些缺陷并提高效率,我们设计了第一个完全分散的单层算法。由于我们的分析以有限的单一度属性为基础,我们还提供了新的一般结果,大大扩展了准点方法的适用性领域。此外,操作者理论方法更有利于执行可实现准确的加速计划,从而可以进一步提高我们预测的趋同率,最终展示了我们量化的方法。