  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.
