We consider the problems of user selection and power control in wireless interference networks, comprising multiple access points (APs) communicating with a group of user equipment devices (UEs) over a shared wireless medium. To achieve a high aggregate rate, while ensuring fairness across all users, we formulate a resilient radio resource management (RRM) policy optimization problem with per-user minimum-capacity constraints that adapt to the underlying network conditions via learnable slack variables. We reformulate the problem in the Lagrangian dual domain, and show that we can parameterize the RRM policies using a finite set of parameters, which can be trained alongside the slack and dual variables via an unsupervised primal-dual approach thanks to a provably small duality gap. We use a scalable and permutation-equivariant graph neural network (GNN) architecture to parameterize the RRM policies based on a graph topology derived from the instantaneous channel conditions. Through experimental results, we verify that the minimum-capacity constraints adapt to the underlying network configurations and channel conditions. We further demonstrate that, thanks to such adaptation, our proposed method achieves a superior tradeoff between the average rate and the 5th percentile rate -- a metric that quantifies the level of fairness in the resource allocation decisions -- as compared to baseline algorithms.

翻译：我们考虑了无线干扰网络中的用户选择与功率控制问题，该网络包含多个接入点（APs），它们通过共享无线介质与一组用户设备（UEs）进行通信。为了实现高聚合速率并确保所有用户间的公平性，我们通过可学习的松弛变量构建了一个具有适应底层网络条件的每用户最小容量约束的弹性无线资源管理（RRM）策略优化问题。我们在拉格朗日对偶域中对问题进行了重构，并证明可以通过有限参数集对RRM策略进行参数化——得益于可证明的小对偶间隙，这些参数可与松弛变量及对偶变量通过无监督原始-对偶方法联合训练。我们采用基于瞬时信道条件导出的图拓扑结构，利用可扩展且置换等变的图神经网络（GNN）架构对RRM策略进行参数化。实验结果验证了最小容量约束能够自适应于底层网络配置与信道条件。我们进一步证明，得益于这种自适应性，与基线算法相比，所提方法在平均速率与第五百分位速率——衡量资源分配决策公平性的指标——之间实现了更优的权衡。