Fast State-Augmented Learning for Wireless Resource Allocation with Dual Variable Regression
This addresses optimization challenges in wireless networks for improved resource allocation, but it is incremental as it builds on existing GNN and dual methods.
The paper tackles resource allocation in multi-user wireless networks by proposing a state-augmented graph neural network (GNN) policy that avoids issues with dual subgradient methods, using dual variable regression for faster inference and improved training, and demonstrates superior performance in transmit power control experiments with proven convergence and optimality gap bounds.
We consider resource allocation problems in multi-user wireless networks, where the goal is to optimize a network-wide utility function subject to constraints on the ergodic average performance of users. We demonstrate how a state-augmented graph neural network (GNN) parametrization for the resource allocation policy circumvents the drawbacks of the ubiquitous dual subgradient methods by representing the network configurations (or states) as graphs and viewing dual variables as dynamic inputs to the model, viewed as graph signals supported over the graphs. Lagrangian maximizing state-augmented policies are learned during the offline training phase, and the dual variables evolve through gradient updates while executing the learned state-augmented policies during the inference phase. Our main contributions are to illustrate how near-optimal initialization of dual multipliers for faster inference can be accomplished with dual variable regression, leveraging a secondary GNN parametrization, and how maximization of the Lagrangian over the multipliers sampled from the dual descent dynamics substantially improves the training of state-augmented models. We demonstrate the superior performance of the proposed algorithm with extensive numerical experiments in a case study of transmit power control. Finally, we prove a convergence result and an exponential probability bound on the excursions of the dual function (iterate) optimality gaps.