Learning Resilient Radio Resource Management Policies with Graph Neural Networks

Abstract

We consider the problems of downlink user selection and power control in wireless networks, comprising multiple transmitters and receivers communicating with each other over a shared wireless medium. To achieve a high aggregate rate, while ensuring fairness across all the receivers, 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 user selection and power control 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 5 th percentile rate-a metric that quantifies the level of fairness in the resource allocation decisions-as compared to baseline algorithms.

State-Augmented Learnable Algorithms for Resource Management in Wireless Networks

“…Through numerical experiments, we show that our proposed state-augmented algorithm, while slightly sacrificing the average performance, significantly outperforms baseline methods in terms of the worst-case user rates, thanks to satisfying the per-user minimum-rate constraints. We also show the benefits of the GNN-based parameterization of the RRM policy in terms of scalability to larger configurations and transferability to unseen network sizes, confirming the findings of prior work using such permutation-equivariant parameterizations [9], [10], [17], [19]- [27].…”

“…We consider both large-scale and smallscale fading for the channel model. The large-scale fading follows a dual-slope path-loss model similar to [17], [31], [32] alongside a 7dB log-normal shadowing. Moreover, the smallscale fading models channel variations across different time steps following a Rayleigh distribution with a pedestrian speed of 1m/s [33].…”

“…As the figure shows, tuning f min reveals the trade-off between the average and worst-case performance of users across all network realizations. Finding the best minimum-rate constraint lower bound is a non-trivial problem, and it has also been shown that this bound can be tuned adaptively based on each specific network realization through the introduction of learnable slack parameters [17], [35], [36]. We leave the incorporation of adaptive minimum-rate constraints into state-augmented RRM algorithms as future work.…”

“…In order to parameterize the state-augmented RRM policy, as in prior work [9], [17], [19], [30], we use graph neural network (GNN) architectures, which have been shown to provide several benefits, such as scalability, transferability, and permutation-equivariance. We operate the GNN over a graphstructured format of the interference channel, defined as a graph G t = (V, E, y t , w t ) at each time step t, where: Fig.…”

“…As a general formulation of the RRM problem, similarly to prior work [6], [9], [16], [17], we consider a network utility maximization problem, subject to multiple constraints, where both the utility and the constraints are defined based on the long-term average performance of users across the network. A common method for solving such problems is to move to the Lagrangian dual domain, where a single objective, i.e., the Lagrangian, can be maximized over the primal variables and minimized over the dual variables, with each dual variable corresponding to a constraint in the original RRM problem.…”